fan edit
n. A version of a movie, song, or other artwork that has been edited by someone other than the original artist, especially by a fan of the work or artist.
Examples
2002
Thanks to digital technology, a delightful new art form emerged this year: the fan edit. Devotees of the pop singer Bjork, for example, have begun running her songs through their computers, tweaking the beats and instrumentation, then posting hundreds of "remixed" versions on the Web. Some of these edits are tone-deaf; others, however, trump the original arrangements. And this summer, Mike J. Nichols, a "Star Wars" addict living in Santa Clarita, Calif., used his Macintosh to make a series of merciful cuts to "The Phantom Menace" — most notably, the virtual elimination of the irksome Jar Jar Binks. Fans who obtained a copy of Nichols's "Phantom Edit" through the Internet hailed the arrival of a vastly improved (if not yet good) movie.
—Daniel Zalewski, “Thinking These Thoughts Is Prohibited,” The New York Times, January 06, 2002
2001 (earliest)
With its obvious parallels to the Napster debate, the shifting of power from the filmmakers to the fans is both disturbing and exciting. It is disturbing because there will no longer be any sort of quality control, aside from the natural assumption that the best "fan edits" will be the ones that get passed around the most. We may have 100 different versions of the next "Star Wars," and 95 of them will be sub-par.
—Daniel Kraus, “The Phantom Edit,” Salon.com, November 05, 2001
Notes
This phrase began appearing in Usenet newsgroups as early as February, 2000.