Well, his magic could give him an edge in many ninja skills. For example, his levitation spell could be used like a ninja's wire technique in a sense. He could also use magic to enhance his physical abilities like speed and strength, similar to how ninjas use chakra. And his magical knowledge of potions could be used to create substances that mimic ninja tools or enhance his performance in battles.
If Harry Potter was raised in Konoha, his magic would blend in an interesting way with ninja skills. His Patronus charm could be used as a sort of summon or distraction in battle, much like how ninjas use summons. His ability to perform magic without hand signs (as he sometimes does in the books) would give him an advantage in quick - draw situations. Also, his magic could be used to heal wounds more effectively than normal ninja medical techniques in some cases.
His magic abilities would likely be a game - changer in Konoha. Harry Potter's ability to apparate could make him extremely mobile, much faster than normal ninja transportation methods. His defensive spells could be used as a form of super - strong jutsu protection. And he might be able to use his magic to detect things that ninjas can't, like hidden magical traps or curses that could be placed in the village.
In terms of offensive magic, he could combine his wizard spells with his demigod powers in unique ways. He might be able to imbue his spells with some of Loki's chaos magic. So instead of a normal Stunning Spell, it could have an added effect of causing confusion or disorientation in his opponents, like a mini - chaos storm. His Apparition could also be affected, perhaps becoming more unpredictable or able to cover greater distances because of his demigod speed and agility.
Harry would probably have a complex relationship with the Uchiha clan. Their Sharingan abilities might intrigue him, and he could potentially share some of his knowledge about mind - related magic with them. He could also form a friendly rivalry with the Hyuga clan. Their Byakugan's ability to see chakra and Harry's ability to sense magic could lead to some interesting exchanges and mutual admiration.
The interaction could be really interesting. Maybe his gamma - related abilities are like a reserve of power for his magic. When he's low on magical energy, his body could automatically tap into the gamma - power to replenish it. And in reverse, his magic could be used to heal or control any negative side - effects of his gamma - abilities. For example, if the gamma - power causes him to lose control sometimes, his magic could be used to calm his mind and bring him back to a more rational state.
Harry's magic could be stronger. Dorea's influence and knowledge of magic could have allowed Harry to tap into his magic potential more easily. Maybe he would be able to perform advanced spells earlier. Also, his magic might have a different 'flavor' so to speak. Since Dorea comes from a different magical background than the Dursleys, Harry's magic could be more attuned to the traditional wizarding ways of magic use.
Well, if Harry Potter was raised by Orochimaru, his magic might develop in a rather different way. Orochimaru is all about experimentation and pushing limits. He might encourage Harry to explore the darker aspects of magic earlier. Harry could end up with a more unorthodox style of spell - casting, perhaps mixing some of the dark arts with traditional wizardry. But he would also have to fight against Orochimaru's more immoral teachings to stay true to his own values.
The magic would be different in that it would have a more ancient and primal feel. Since Alduin is an ancient and powerful entity, Harry's magic would be influenced by that. It wouldn't be limited to the rules and regulations of the wizarding world. He could potentially have the ability to transform into something more dragon - like, or at least gain some of the physical attributes of a dragon. His magic would be a blend of his own wizarding heritage and Alduin's otherworldly power, creating a completely new and unique form of magic that is both terrifying and awe - inspiring.
His magic would likely be more water - based. He might be able to conjure water - made weapons or shields more easily. For example, he could create a spear made of enchanted water that can pierce through dark magic defenses.
Sam and Dean Winchester would interact with Harry like a big brother - type relationship. They would be protective of him, and teach him things. For example, Dean might show Harry how to use a gun while Sam could help him with research, both magical and non - magical. Harry would likely share his knowledge of magic with them, which would be fascinating for the Winchesters. He could also introduce them to his friends from Hogwarts like Hermione and Ron, and there would be some interesting cultural clashes between the hunter and wizarding cultures.
The interactions would be really fascinating. Harry could introduce his Hogwarts friends to things like the Ninja Way. Hermione would probably analyze it from a theoretical perspective, while Ron would be more interested in the practical side, like any new spells or skills. The teachers at Hogwarts would also have to adapt to Harry's different approach. For example, Snape might be even more critical at first, but as he sees the positive aspects of Harry's Naruto - influenced growth, he might change his view slightly.
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.