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What about Adaptation Displacement ? I found it in the disambiguation page for Weird Al Effect . I think Covered Up is what you’re looking for.
Edited by CSS1
It's not a cover though, it's the original song licensed for use in the show.
I do some cleanup and then I enjoy shows you probably think are cringe.
Older Than They Think can include songs, and the Music subpage already has one example along the lines you describe: House licensed "Teardrop" by Massive Attack to use as the opening theme, and now a lot of people incorrectly assume it was written specifically for the show.
I didn't write any of that.
What trope best fits this scenario? A work uses a song in its soundtrack that people think was made for the show, but it was actually already a song.
Older Than They Think seems more about story stuff, not music... it doesn't fit Parody Displacement, that's for, well, parodies... Colbert Bump could fit but I'm thinking about the mistaken identity part. Common Knowledge might work?