You can try looking on fanfiction websites like Archive of Our Own (AO3). It has a vast collection of fanfictions from various fandoms, and there's a good chance you'll find 'Joker adopts Harry Potter' ones there.
One interesting aspect could be how the Joker's chaotic nature would contrast with the magical world of Harry Potter. For example, he might use his wacky sense of humor to disrupt the strict rules at Hogwarts. He could turn Defense Against the Dark Arts classes into his own little shows, much to the dismay of the professors.
I'm not sure if there is a specific instance where a 'Joker' would be directly involved in raising Harry Potter fanfiction. Usually, fanfiction is created and promoted by fans themselves within the fan community, not by a character like the Joker.
Well, if we're talking about the Joker from the Batman universe, there's no canonical information indicating he has any knowledge of Harry Potter fanfiction. He's more preoccupied with chaos in Gotham. But in some wild crossovers in fan - created works, he might be depicted as knowing it, just for the fun of mashing up different universes.
The Joker as a professor in Harry Potter fanfiction? That's a wild idea. He could be the professor of Dark Arts in a very different way. Instead of the traditional Dark Arts that the wizarding world knows, he would introduce his own form of 'dark art' which is more about psychological torture and mind games. His classes would be full of his maniacal laughter and unexpected challenges. Students would have to constantly be on their toes, not knowing what he'll do next. He might even use his students in his elaborate schemes against the other professors or the Ministry of Magic.
Perhaps Bruce Banner adopts Harry Potter after the events at Hogwarts. He takes Harry to the world of science, showing him things like advanced laboratories and scientific research. Harry, in turn, shows Bruce the wonders of magic. Their bond grows as they learn from each other, and together they face new threats that combine elements of both the magical and scientific worlds.
It could be a young wizard who lost their parents during the final battle against Voldemort. Harry feels responsible for all the orphans created by the war and decides to take this particular child under his wing.
Another theme is self - discovery for Harry. With the influence of the MC, Harry gets to explore different aspects of himself. For example, he might discover new magical abilities or gain more confidence in his identity as a wizard. In some fanfictions, the MC helps Harry to look beyond what he thought was possible for himself.
One possible plotline could be that Harry, after some dark magic influence or a strange accident, starts to show Joker - like behavior at Hogwarts. He might play cruel pranks on his classmates and teachers, using his magic in unexpected and unethical ways.
One common theme is the clash of two different worlds. The orderly and magical world of Harry Potter with its own set of rules and the chaotic, lawless world that the Joker represents. Another theme could be the corruption of innocence. The Joker might try to influence the young wizards and witches at Hogwarts, corrupting their pure intentions.