Fanfic is in a number of dictionaries, and is used in a variety of publications, though probably not as frequently as the full phrase
fan fiction.
An example, from the
Globe and Mail (Canada) in April this year:
In the end, Schmicago is primarily musical-theatre fanfic linked by Paul’s amusing song parodies (which skirt close to full-on Weird Al territory at times this season).
This genre of writing seems to have had its origin in the science fiction field. The online
Historical Dictionary of Science Fiction has the earliest citation of
fanfic from 1968, and the earliest usage example of
fan fiction from 1938.
In earliest usage,
fanfic was simply amateur fiction - written by SF fans and published in fanzines. Over time, a more specific meaning developed: amateur fiction using characters and/or settings from commercially published works.
I'll add
fanfic as a rare word.
(RTT: this isn't the first time I've accepted a word formed by this type of clipping.
Satnav comes to mind. I feel that
sci-fi is the usual form, but feel free to submit a suggestion.)