Cryptomnesia, according to Wikipedia, is “a memory bias whereby a person falsely recalls generating a thought, an idea, a song, or a joke, when the thought was actually generated by someone else”.
Newsweek has an article discussing this phenomenon; including what appear to be genuine cases of cryptomnesia and the novel tests being conducted by psychologists to uncover them.
When people engage in creative activity, they are so involved in generating or coming up with something new or novel that they fail to protect against what they previously experienced. […]
It’s easier to remember information than it is to remember its source. Under the right conditions, this quirk can even evoke false memories. […]
But misattributing memories from one source to another, whether from imagination to reality or from a friend to oneself, is only one of the psychological quirks behind unconscious plagiarism. Another is implicit memory, which Dan Schacter, a psychologist at Harvard, called, “the fact that we can sometimes remember information without knowing that we’re remembering it.”
All of the famous cases of cryptomnesia are mentioned (George Harrison, Nietzsche), but one: Richard Nixon’s wartime experiences that were later traced to Hollywood movies.
via Mind Hacks