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Characters reveal their secret identity, but the confidants aren't buying it/assume they're joking
(lemmy.world)
Superman TAS: Lois Lane asks Clark Kent how he always gets the best stories. Clark slyly tells her that he gets up close to the action constantly because he's actually Superman, to which Lane merely replies "You're a sick man, Kent."
Lucifer (show): The real archangel Lucifer runs a nightclub on Earth in Los Angeles. He constantly tells people, including the police, that he's the devil. Everyone assumes he's being metaphorical or grandiose.
Batman (Gotham Adventures v1 #35): Bruce Wayne can't ethically testify in court against someone he helped imprison as Batman, so he confesses his identity. Everyone simply laughs, and the judge sternly tells him off for joking.
Since the other two posts on this community have examples from Breaking Bad, I'll add that to this one:
Walt admits to Hank on two occasions (iirc) that he's up to some illegal activities. In the first season, I think when Hank helps him load some duffel bags full of cash into his car, he asks what's in the bags. Walt says, "Half a million in cash," and then they share a laugh.
In a later season, when Hank finds Gale's notebook is tributed to "W.W", Hank jokingly suggests maybe it stands for "Walter White". Walt puts his hands up and says, "You caught me."