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The closest thing I found is Historical Character's Fictional Relative. Although the trope seems to imply that the character should actually be a relative, I'd personally call it close enough if the entire main plot is based on legitimately trying to prove this. Even if it's disproven in the end, it might be a Subverted Trope ("I'm definitely the son of JFK and I'll definitely prove it! ... Oh, turns out I'm actually not. Huh.")
Is this related to the "my uncle works at Nintendo" meme?
A person commits Suicide by Cop. Investigation turns up 2 more dead people, and eventually the suicide is determined to have been related to a failed robbery of one of the other dead, who collected presidential artifacts. The actual item desired by the mastermind of the robbery (still alive) is a lock of JFK's hair, by which (he believes) a simple DNA test would prove he's an illegitimate son of JFK.
Famous Ancestor, subverted?
A person believes himself to be an illegitimate son of John F. Kennedy, and is desperate to prove it.