To answer this question, you have to dig into the bowels of some pretty authoritative mid-90s fan sites. Fear not, I've done it for you!
It was created specifically for the show, according to Chris Carter (X-Files creator) while donating memorabilia to the Smithsonian National Museum of American History.
Where did the "I Want to Believe" poster from Mulder's office come from?
It [the poster donated to the Smithsonian] came from Gillian Anderson's collection. All the rest of the original posters had been stolen or, I assume, destroyed.
The original graphic came from me saying, "Let's get a picture of a spaceship and put—Ed Ruscha-like—"I want to believe." I love Ed Ruscha. I love the way he puts text in his paintings. (I actually got to say to him, "I was inspired by you.") When I saw the [finished] poster I recognized the photograph because it came from a series of photographs taken in Europe by a guy named Billy Meier. And I said, "Did we get the clearance for that photograph?" And they said, "Oh, yes!" Ten years went by and all of a sudden I got a call from Fox legal: "We have an intellectual property lawsuit we have to depose you for." And there was a lawsuit and they had not done the proper clearance for that photograph.
Some other links supporting this:
On this fan site, the author says of the poster:
It has become something of a Holy Grail for fans of the show. Many X-files fan would like a copy of the poster, but unfortunately it was a one off produced for the X-files production team.
There are made up versions of the poster available, but standards vary, good luck if you are looking for a copy.
There have been a couple of explanations for why the poster changed a couple of times over the series (without any in-world mention). Both of them point to the theory that the poster was made specifically for the show and was not a mass-produced product.
Frank Spotnitz (X-Files writer/producer) explained to popcornmonster.com:
My recollection is that there was a problem with the legal rights to the photograph used in the original ‘I Want To Believe’ poster. It was resolved by changing the image.
According to The X-Files Trivia on IMDB this poster was a hot item on set:
Props from Mulder's X-Files office are currently preserved and on display at the Hollywood Entertainment Museum in Los Angeles. According to the museum, the famous I Want to Believe UFO poster from the office continually had to be replaced as copies kept disappearing from the set. The poster on display at the museum is reportedly one of the last available copies of the original set-used posters.