Kathryn Heisenfelt - Ann Sheridan and the Sign of the Sphinx (1943)
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When I first stumbled across this title I thought it's not that Ann Sheridan but in fact it is Ann Sheridan the actress which might make this an early instance of fanfic (despite the claim of "authorized"). Instead it's more what might be called personality fiction where a story or film is based on a living person as more or less their self. (If the personality isn't living then it's historical fiction.) There aren't many examples really except stray promotional items or one-offs like Being John Malkovich. The most sustained attempts are in comics - series based on John Wayne (82 issues, 1950-57), Jerry Lewis (84 issues, 1957-71), Tom Mix (61 issues, 1948-53), Bob Hope (109 issues, 1950-68) and so on.
Still "Ann Sheridan" might not matter much - the book looks like the story wouldn't really change if her name was replaced. The interior illustrations don't even resemble her. This was one of 16 titles in a series published by Whitman in the 1940s, most written by Heisenfelt and all featuring a media personality. (There's an overview at this site.) Shirley Temple and the Screaming Specter and Judy Garland and the Hoodoo Costume sound more like modern spoofs and it's too bad those aren't online.