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.
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.
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.
In such a fanfiction, Harry Potter could bring a new perspective to Arkham Asylum. He has faced dark wizards and dark magic, so he might see similarities in the deranged minds of the asylum's inmates. His Gryffindor courage would lead him to explore the place, perhaps making unexpected alliances with some of the more misunderstood inmates, all while trying to keep his magical identity a secret to avoid chaos.
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.
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 plot could be Harry exploring the dark secrets of Arkham Asylum. He might encounter various infamous inmates and try to survive their threats while also uncovering a conspiracy within the asylum's walls.
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.
One great 'Batman Arkham Asylum' fanfiction is 'The Dark Knight's Redemption'. It delves deeper into Batman's psyche as he battles his inner demons while trying to escape the asylum. The author does a great job of capturing the dark and gritty atmosphere of the game.
In this fanfiction, Naruto could be a patient in Arkham Asylum. He has lost his memory and believes he is in some strange version of Konoha. The doctors at the asylum are trying to understand his 'delusions' about ninjas and chakra. Meanwhile, some of the more evil inmates sense his power and try to manipulate him for their own gain.