Well, in such a fanfiction, Harry would likely face a lot of challenges different from his original story. He'd be exposed to the insanity and chaos of Arkham. His Hogwarts - like education might be replaced with learning to survive in a place full of villains. He could potentially develop a very different set of skills and a much more cynical view of the world.
Well, he'd probably be exposed to a lot of chaos and madness. He might develop some very different magical skills, perhaps ones influenced by the dark and deranged atmosphere of Arkham. He could also have a very warped view of the wizarding world compared to what we know from the original series.
In this fanfiction, the interactions would be full of tension. Harry would be like a fish out of water in Arkham. The villains in Arkham, such as the Joker or Harley Quinn, could have very different reactions to Harry. The Joker might see him as a new plaything to toy with, while Harley Quinn might show some sympathy towards him. And Harry would have to constantly navigate these dangerous relationships while also trying to figure out his own identity in this strange new world.
One possible plotline could be her discovery of magic in the dark and chaotic environment of Arkham. Maybe she has to hide her magic from the more sinister characters there. Another could be her forming an unlikely alliance with some of the inmates who have a sense of justice, and together they help her escape Arkham to find her place in the wizarding world.
His magic might be darker. The environment of Arkham Asylum is full of negative energy. So, it could taint his magic in some way, making it more aggressive or unpredictable.
Well, she would be much more hardened. The original Harry grew up in a relatively normal, albeit unloving, muggle household. But a female Harry in Arkham would have seen and experienced true horror and madness from a young age. So she'd be more cynical and less trusting.
In many Harry Potter fanfictions, the concept of being 'raised by darkness' can take various forms. It might involve a character being brought up in an environment influenced by dark magic or dark wizards. For example, a character could be raised in a family that secretly practices the Dark Arts. This could lead to the character having a different moral compass compared to those raised in the light. They may struggle with the line between right and wrong, as their upbringing has exposed them to unethical magical practices.
Well, you could create a fanfiction where the dementors in the Harry Potter universe are somehow related to the Scarecrow's fear toxin in Arkham Knight. Picture a scenario where the heroes from both worlds have to figure out how to combat this new, combined threat. Also, a story about Hermione using her intelligence to analyze the technology in Arkham Knight's Gotham and applying her magic in innovative ways to help could be really cool.
The more intelligent inmates, like the Joker if he were there, might be intrigued by Harry. They would want to figure out how his magic works and might try to use it for their own devious plans. Others might see him as a savior, someone who could get them out of the asylum with his magic.