On the left is the Fairfield letter mailed on December 16th 1969. 
Nine days prior to this communication another Fairfield letter was received, dated December 7th 1969 (see below). It is highly likely, based on the handwriting and tone of each correspondence, that they were penned by the same hand. Many have questioned these two letters as being genuine Zodiac material, however, there is every reason to consider them as being true Zodiac correspondence based on several factors.
Without knowledge of these 'dubious' letters existence or having seen them in any newspapers, it would be uncanny how the Zodiac Killer would continue the theme of these two letters into the 'Melvin Belli' letter on December 20th 1969, the 'My Name is..' letter on April 20th 1970 and the 'Button' letter mailed on June 26th 1970. In other words, three of his next four communications. Here is the theme running consecutively, starting with the December 7th 1969 letter: 
"I just need help. I will kill again so expect it any time now. The will be a cop. Then I will turn myself in OK. I will kill in SF 3 times (including cops). The one thing I ask of you is this, please help me. Please help me I cannot remain in control for much longer. But there is more glory in killing a cop than a cid because a cop can shoot back. I shot a man sitting in a parked car with a .38".
It is clear from the December 7th and 16th communications the author is threatening 'government life'- most likely the police. In the December 7th 1969 communication the author has supplied a code containing 38 characters, followed by the December 16th 1969 letter threatening another 38 kills including cops, and curiously in his June 26th 1970 'Button' letter, the claim of shooting "a man with a .38." Most likely coincidence, but you never know. 
Here is a forum thread on Zodiac Killer Site with some of the same salient observations, particularly by AK Wilks.
The 38 character December 7th 1969 Fairfield letter (below) has been cleaned up and darkened to make the letter more readable. Not all the code is very clear, so has been interpreted from what we know of the Zodiac Killer's other codes and ciphers (The final line could hold a 'boxy style' C, but has been interpreted as a square. The B on the second line is also questionable).   
"I just need help. I will kill again so expect it any time now. The will be a cop. Then I will Turn myself in    OK."

Was this code a crude attempt at pushing us in the right direction regarding his infamous 340 character cipher mailed just one month earlier. The obvious similarities are there, particularly the first four characters of this code mimicking the opening four characters of the 340 cipher, and the last five characters of each code in both instances. It certainly isn't difficult to spot an inference to 'Zodiac' once again, possibly indicating its importance within the 340 cipher. 
A hoaxer could easily have copied elements of the 340 cipher and incorporated them into, what many believe, a poor imitation of a Zodiac correspondence. But if the Zodiac Killer hadn't seen either of the two Fairfield letters, do we attribute the continuing theme through three of the next four genuine Zodiac correspondences as just sheer luck, referring to "needing help" and his suggestion of "killing a cop."  Additionally, from the 'double event' November 8th/9th 1969 contact, we have effectively been given four ciphers or codes (whether crude or not) in five correspondences. 
These observations may lend more credence to the Fairfield communications, and their rightful place as having been penned by the hand of the Zodiac Killer. 
​THE MESSAGE WITHIN THE FAIRFIELD LETTER

'Rubislaw,' a regular contributor to this site, inspired me to take another look at the Fairfield letter, mailed on December 16th 1969.
​The correspondence stated "This is the Zodiac speaking. I just want to tell you this state is in trouble..I will go for the Goverment life, so don't foreget me. I will kill more people than you cops can count, so look for more blood. You better print."
The author then added the trademark crosshairs with a small code. The crosshairs had the same symbol in each of the four quadrants, with five symbols to its left. Decoding such a small sample could never be authenticated, however, an attempt will be made later in this article. 
The author attached a drawing of blood dripping from a knife, entitled "The Bleeding Knife of Zodiac."  Zodiac had previously claimed seven victims in the Bus Bomb letter mailed to the San Francisco Chronicle on November 9th 1969, so it wasn't surprising to see this knife drawing had 8 drops of blood falling from the blade. See here.
It is extremely difficult to pinpoint the inspiration for this letter, but here are a few notable events in December 1969.
The first being the murder of Meredith Hunter at the Altamont Free Concert on December 6th 1969 at the hands of Hells Angel Alan Passaro, who fatally stabbed and beat the 18 year old to death after he produced a revolver. This is not insinuating Alan Passaro was the Zodiac Killer, but bearing in mind the Hells Angels connection on Warren Avenue, Vallejo, and the drugs bust at The Cottage on Lake Herman Road in the run-up to the murders of David Faraday and Betty Lou Jensen, it was worth mentioning. Alan Passaro was later cleared of the murder, having deemed to have acted in self defense.
​ 
On the political front, bearing in mind the author was threatening to go for 'government life,' was the author referencing the troubles of the day. On December 1st 1969 the Selective Service System of the United States conducted two lotteries to determine the order of call to military service in the Vietnam War for men born from 1944 to 1950. These lotteries occurred during a period of conscription from just before World War II to 1973. It was the first time a lottery system had been used to select men for military service since 1942. The lottery numbers assigned in December 1969 were used during calendar year 1970 both to call for induction and to call for physical examination, a preliminary call covering more men. Taken from Wikipedia. For those believing in a Vietnam or military connection to Zodiac, was he responding with outrage to this lottery based conscription- threatening to attack 'government life'.
 
On December 12th 1969, the Desert Sun ran an article about 'Two Attorneys Jailed in Tate Murder Case.'
District Judge David Brown today sentenced two Los Angeles lawyers to 72 hours in jail and fined them $lOO each for trying to make a “press spectacular” out of the case of Charles D. Watson, charged in the Sharon Tate murders. "I am fining you $lOO and jailing you for 72 hours but I will suspend this provided you take the next plane back to California and shut your mouths,” Brown told the attorneys, Perry Walshin and David DeLoach. “I admonish you for making a circus out of my courtroom,” said the judge. Watson, dressed in green work clothes, made his first public appearance since he gave himself up Nov. 30 in I answer to a California murder I warrant. He since has been indicted on seven counts of murder and one count of conspiracy. Susan Denise Atkins, another, of a hippie band charged in the California murders, told a grand jury Watson was the one who killed Miss Tate with a knife. “Do you want to talk to these men or be represented by them" Judge Brown asked Watson today about the two California lawyers. “No, sir, I do not,” Watson said. “Do you want to see them” Brown asked. “No, I do not,” Watson replied. At least 30 Texas highway 1 patrolmen guarded Watson. At least 20 patrolmen and sheriffs deputies were in the courtroom. Watson, who grew up at nearby Copeville, Tex., was moved into the courtroom before 6:30 a. m. and no reporters or photographers were allowed near him. Leaving the courtroom, officers threw a coat over Watson’s head and hustled him past photographers. Walshin and DeLoach came to Texas last week. Walshin said he had represented Watson on the coast and that Watson’s mother wanted him in the case. link.

This article was published four days before the Fairfield letter and eight days before Zodiac's letter to attorney Melvin Belli.
Was the Fairfield letter actually written by somebody connected with the Manson Family, or an avid follower of the unfolding events. Tex Watson would ultimately be convicted of the seven counts of first degree murder he was charged with. The eight drops of blood on the 'bleeding knife' threatening a further murder, using Zodiac as the outlet.  
These are three unlikely examples of a possible inspiration for the Fairfield letter. Please post any further ideas in comments.

The final observation is regarding the code. The Zodiac Killer mailed the 'Halloween' card on October 27th 1970.
Was the Fairfield letter, if a Zodiac correspondence, the precursor to this card in rudimentary form. The Fairfield letter had four identical symbols in the four quadrants of the crosshairs. The 'Halloween' card contained four methods of death in the four quadrants, bisected by Paradice and Slaves, not dissimilar to the Fairfield letter.
Tahoe27 discovered a connection between a Tim Holt comic and the 'Halloween' card, regarding the wording  By Fire, By Gun, By Rope and By Knife. Is it possible the Fairfield letter symbols around the crosshairs represented these four methods of death? But what of the five symbols to the left. Take a look at the Tim Holt picture above.  

On the 'Dripping Pen Card' mailed on November 8th 1969 the Zodiac left us his running victim count, but this time he provided us several pointers by displaying the months. He wrote "Des, July, Aug, Sept, Oct = 7."  We know of Lake Herman Road (2) in December, Blue Rock Springs Park (1) in July, Lake Berryessa (1) in September and Presidio Heights (1) in October. That is five murders out of the seven he was claiming. That meant he was indicating either two murders in August, or just one in August and another in either of the other months. One consideration was the murder of Cheri Jo Bates on October 30th 1966, that he would belatedly claim in a future correspondence. However his statement in the November 9th 'Bus Bomb' letter is telling: "This is the Zodiac speaking up to the end of Oct I have killed 7 people." This likely meant "This is the Zodiac speaking up to the end of Oct 31st 1969 I have killed 7 people. This doesn't necessarily rule out the Cheri Jo Bates murder, however without proof this is a Zodiac murder, or a murder under the umbrella of Zodiac, it is a curious statement.
Why did the Zodiac Killer specify the end of October, when his most recent murder by all accounts was the brutal slaying of Paul Stine on October 11th 1969. This could be interpreted as a sixth murder in August, and a seventh murder between October 11th 1969 and October 31st 1969. He would expand in his correspondence "I thought you would need a good laugh before you hear the bad news, you won't get the news for a while yet."  In view of his 'Bus Bomb' letter declaration that he would "change the way the collecting of slaves. I shall no longer announce to anyone. When I committ my murders, they shall look like routine robberies, killings of anger, + a few fake accidents, etc," this seventh murder may have been committed in the latter two thirds of October, detailed in the total, but not elaborated upon, and the suggestion that we wouldn't get the bad news for a while was somehow related to how or where the person was killed.     

There is however a completely different alternative, bringing into play the Melvin Belli letter on December 20th 1969. This correspondence stated Zodiac was in danger of looking for a ninth and tenth victim. The assumption therefore, was that victim number eight was probably killed sometime between the 'Dripping Pen' card on November 8th 1969 (or possibly November 9th), claiming seven victims and the Melvin Belli letter mailed on December 20th 1969. But again, taking the latter 'Bus Bomb' communication, Zodiac had claimed seven victims to end of October, not up to November 9th 1969. He did state seven victims on the 'Dripping Pen' card, but he added the extra hint that "you won't get the bad news for a while yet."
This may suggest that indeed, he had already killed again, prior to November 8th, but he simply wasn't announcing it to anybody, as the following communication would testify. We know that by the end of October (31st) the total was seven, therefore this unannounced eighth murder would had to have been committed from November 1st 1969 up to November 9th 1969. 
A contested piece of correspondence was the 'Fairfield' letter on December 16th 1969, claiming "I will go for government life." The accompanying drawing depicted the 'Bleeding Knife of Zodiac,' with eight drops of blood dripping from the weapon, suggestive of an eighth victim. Was this indicative of another Zodiac murder by knife, having been bolstered by his 'successful' attack, in theatric style, on Bryan Hartnell and Cecelia Shepard on September 27th 1969 at Lake Berryessa. Or was the knife just a reminder to his last crime we know he committed. If this correspondence was genuine, the term 'government life', may indicate any person in any state run organization, and a distinct hatred towards officialdom, which is unsurprising bearing in mind previous communications.
The question being, can anybody find the eighth murder spanning November 1st 1969 to November 9th 1969, in a relevant geographical location, that doesn't have the hallmarks of Zodiac. After all, he did state he would "change the way of collecting the slaves".  If this were the case, we simply wouldn't recognize it anyway.  

# A Salesian High School teacher, Daniel Williams had his house broken into, but nothing was taken. A man claiming to be the Zodiac Killer made several threatening phone calls beginning on October 23rd 1969, culminating with the caller saying "You're the dead duck" on November 2nd 1969. Later that day Williams took a drink from the refrigerator, but fortunately spat it out after noticing a metallic taste. The drink contained enough arsenic to kill. Would a teacher be considered 'government life'. The date fits the criteria and the death could have appeared like natural causes, or a killing of anger.
Daniel Williams residence was situated at 1234 Bush Street, Martinez, only 9 miles from the location of Zodiac's first crime at Lake Herman Road.
http://www.zodiacciphers.com/zodiac-news/youre-the-dead-duck

An article in the San Francisco Chronicle by Paul Avery dated November 12th 1969 and titled "I've Killed Seven, The Zodiac Claims", clearly states 'As proof the letters were from the true Zodiac and not an imposter, the mass murderer enclosed another portion of the piece of shirt he tore off the body of San Francisco taxi driver Paul Stine'. Then in a second article on December 28th 1969 entitled "New Zodiac Letter...Fears He'll Kill Again", it states 'A few days after the Stine killing, Zodiac sent a letter to San Francisco newspapers and also included a swatch of Paul Stine's shirt. Another letter and another piece of Stine's shirt was sent to a Newspaper on November 11th'. See here. The 340 Cipher and Dripping Pen Card/Bus Bomb Letter were mailed in close succession on November 8th and 9th at the weekend and may have arrived at the beginning of the following week, accounting for the November 11th attribution. Then a Youtube documentary commencing at the 3 minute mark confirms that a total of three shirt pieces were sent. Two articles and one documentary, all indicating that a third section of Paul Stine's was sent accompanying either the 340 Cipher or Bus Bomb Letter.
Had the Zodiac Killer set aside three portions of shirt to send, it is highly unlikely he would want to be sitting on incriminating evidence for too long and after the murder of Paul Stine in Presidio Heights on October 11th 1969 he would mail his three portions of shirt with his next three correspondences. His first being the October 13th letter, just two days after the murder, his next letters were postmarked within one day of each other, so he sent the second portion with these and the final piece was mailed with the Melvin Belli Letter on December 20th 1969. What he didn't do however, was mail a piece of shirt with the Fairfield Letter on December 16th, four days before the Melvin Belli Letter, why, because it was a fake Zodiac letter, not mailed by the killer. This is not conclusive, but other features of the Fairfield Letter, suggest this correspondence was mailed by an impostor, who knew little about the mind of the real serial killer. 

It cannot be known for certain, but the Fairfield Letter seems to be suggesting a link to the Lake Berryessa stabbing on September 27th 1969, the only crime committed thus far with a knife. It was always questioned why the Zodiac failed to brag about his theatrical crime on the shoreline of Lake Berryessa, after all, it was his most daring to date. There is no definitive answer, but one thing the Zodiac Killer never foresaw, was that he was to leave a surviving witness, in Bryan Hartnell. He could have bragged endlessly about this crime, but in hindsight his failure to kill both victims actually played right into his hands. The detailed account of Bryan Hartnell, the description of the killer's costume and the extensive newspaper accounts, gave him all the publicity he could ever have wished for. What more was there to add. However, newspaper accounts were starved of the full details, in that the 'by knife' writing on the car door of Bryan Hartnell's car was withheld, probably to flush out the real killer from any subsequent hoaxers, and the Fairfield Letter may be one example.
Anybody who was aware of the Lake Berryessa attack could have concocted the phrase 'The Bleeding Knife of Zodiac', and more importantly its failure to highlight 'by knife' was an opportunity missed from a killer now determined to link himself to the authenticity of his correspondence, by enclosing the swatches of Paul Stine's shirt. The Zodiac Killer had his ego dented when his first cipher was cracked in a matter of days by schoolteacher Donald Gene Harden and his wife, Bettye June Harden, two amateur sleuths. His response was to send us the still unsolved 340 Cipher, crafted either with no solution or a solution that went far beyond simple homophonic substitution. The Fairfield Letter however, is a retrograde step into mediocrity, when the supposed Zodiac Killer now reverts back to scribbling nine symbols, showing little effort, in the apparent guise of a small code and beginning his letter with "I just want to tell you this state is in trouble, I will go for the government life", more reminiscent of a political agenda, with bold claims of another potential 38 victims. The 'knife' wording does look similar to the writing on the card door at Lake Berryessa, but the template for these letters was freely available throughout his correspondence up to this point. But he fails to corroborate this letter with a swatch of Paul Stine's shirt, why, because the real Zodiac Killer was to contact authorities just four days later.   

The Fairfield Letter was mailed on December 16th 1969, sandwiched between the Bus Bomb letter of November 9th and the Melvin Belli letter on December 20th and it was this reason, along with its design that has placed this relatively early letter into the section of unlikely Zodiac correspondence. The main reason for this centers on the belief that the Zodiac Killer, after murdering Paul Stine in Presidio Heights on October 11th 1969, actually mailed three pieces of Paul Stine's shirt to the newspapers, not two as is widely believed. This is not a new concept and there is a thorough section devoted to this on the excellent ZodiacKillerSite forum here, but for those who have not come across this, we shall do a brief summary, before bringing the Fairfield Letter into the equation.
It is widely acknowledged that two pieces of Paul Stine's shirt were sent, firstly to the San Francisco Chronicle on October 13th 1969, just two days after his murder and secondly on December 20th 1969 to the home residence of prominent attorney Melvin Belli, but it was likely a third piece was sent along with the '340 Cipher and Dripping Pen Card' on November 8th 1969 or Bus Bomb Letter a day later, outlined in two articles written by the San Francisco Chronicle and mentioned in a Youtube documentary. Anyone can believe in mistakes, but the wording in the Chronicle is specific, to say the least and the mailing of three portions of Paul Stine's shirt makes perfect sense, from photographs of the shirt on the Zodiac Killer Facts site marked A, B and C. 
Here is an excerpt from the FBI files (Zodiac 5 page 46/249), clearly showing three shirt pieces were mailed.