Tim Drake adopted early au. But not by the man you think (aka early Joker Junior)
-Unknown when or how long Joker has had Tim, but it's been for a long time. (Unsure of when to make Joker's acquirement of Tim really)
-Usually kept in some hideout for long stretches of time, which is pretty much his only sense of home. He gets checked up on occasionally by henchmen or Harley since Joker doesn't have a practical use for him all the time.
-Has a civilian disguise of Timothy when he's out in public to match Joker's. His act is to be an innocent child, sometimes pretending to be lost, or just to help make Joker's message very clear. Tim is scarily good at switching seamlessly into the persona.
-Also still knows about the secret identities of the bat family, just can't sneak out to see them as much, he idolizes them just the same though.
-He can't take pictures since he doesn't own a camera either, but uses newspaper clippings or swipes the random pictures hencemen would have of them.
-Although it's not like he isn't taking advantage of all that time alone either, he still sneaks out sometimes to spy on the bats. It is absolutely terrifying each time though.
-Soon gets caught by Robin and thought to be a very ill child from his complexion (very pale from constant exposure to joker gas, and some accidents here and there, and the overall Not Normal upbringing look)
-And after that, it falls into the same situation as Tim being Robin. Joker has no idea about Tim's secret hangouts with the Bats. The bats are trying to figure out Tim's situation and how to help but Tim doesn't want to give up that information. And he is just trying to keep above it all.