Well, first of all, his magic might be more secretive. In Arkham Asylum, he'd have to hide his magic from the inmates and the staff. This could lead to him developing a more stealthy way of using it. Secondly, the chaos of Arkham could make his magic more adaptable. He'd have to deal with all sorts of unexpected situations, so his magic would need to be able to change quickly. And finally, the psychological impact of Arkham could lead to his magic being tied to his emotions in a very different way. For example, his anger or fear might fuel his magic in ways that are not seen in the normal Harry Potter universe.
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.
If Harry was raised in Arkham Asylum in fanfiction, his magic could be influenced by the constant madness around him. He might use it in self - defense more often, leading to a more instinctive and less refined use of spells. Also, he could learn to combine magic with the 'tricks' he'd pick up from the inmates to create some truly strange and unorthodox magical techniques.
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.
Harry's personality would be greatly influenced. He would be more polished in his behavior, as Narcissa would demand propriety. He might be less likely to take risks without thinking, as Narcissa would have instilled in him a sense of caution. His sense of loyalty would be more complex. Instead of the straightforward loyalty he has in the original story, it could be divided between Narcissa's family values and his own sense of right and wrong. Also, he may have a more aristocratic air about him, with a refined way of speaking and interacting with others.
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.
When raised by an Acromantula, his magic could be attuned to nature in a different way. He might be able to use magic related to the forest and spiders more easily. His magic could have a more primal feel to it, as he learned from a creature that is not part of the wizarding human society. He could also have a natural ability to sense danger in the forest, which could be an extension of his magical abilities.
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.
His magic could be more combat - oriented. Jiraiya's ninja background would likely influence Harry to use magic in a more direct and aggressive way in battles, rather than just for defensive or utility purposes like in the original series.
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.
Harry might have an easier time with spells related to transformation. Just as Poseidon can change the form of water, Harry could be more adept at transfiguration spells. He could also have a natural ability to breathe underwater and perform magic while submerged, which would be a huge advantage in certain situations. This would open up new possibilities for him in both the wizarding world and any underwater adventures he might have.
His magic would probably be more esoteric. Since Zelretch has knowledge of different kinds of magic, Harry could learn spells or abilities that are not part of the normal Hogwarts curriculum. He might be able to manipulate time or space in ways that other wizards can't.
If Hidan raised Harry Potter, Harry's magic development would be very different. Hidan doesn't value the traditional ways of learning. So Harry might learn magic through trial and error in real - life dangerous situations. His spells could be more improvised and less refined in the traditional sense. For example, instead of learning the proper wand movements for a spell in a classroom, he might learn how to quickly cast a spell while being attacked. This could make his magic more instinctive but also less precise in some aspects.