Best I can think where the character is actually the protagonist would be American Psycho 2 (except that’s a movie… and a movie that is… not very good). As for just having female psycho characters, you could probably count Cozy Glow from MLP, except she’s less of a womanchild and more of an actual child, though I’m guessing that’s probably not what you’re looking for. XD Quinella from SAO:Alicization could also probably be counted as a psychopath, though I’m not sure how widespread that interpretation is. Though tbh most of this comment is irrelevant since you said protagonist. XD