Maybe Harry's magic gives his cousin a sense of security. If the cousin was always in some kind of danger, Harry could use magic to keep him safe. This would make the cousin less fearful and more adventurous. He could start to explore the world around him more, knowing that Harry has his back with magic. In addition, the cousin might develop an interest in magic himself, which could change his whole perspective on life.
In this fanfiction, Harry's magic might influence his cousin in a very personal way. It could be that Harry uses magic to heal some emotional wounds of his cousin. For instance, if the cousin has some past traumas related to family or school, Harry's magic could be used in a way to soothe those pains. This would lead to the cousin becoming a more well - rounded and positive person. He may start to see the good in others and in life in general because of the positive impact of Harry's magic.
In some fanfictions, it could be through intense emotional experiences. For example, when he faces a great loss or discovers a deep truth about his family, it triggers something within him and unblocks his magic.
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.
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.
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.
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.
Since Madame Maxime would expose Harry to different magical cultures, his magic could develop in a more diverse way. He could have a better understanding of magic related to magical creatures, like using magic to communicate with veelas or control giants. This would be different from the more traditional Hogwarts curriculum that focuses mainly on spells for general use. His magic could also be more attuned to the environment of the French wizarding world, which might have different ley lines or sources of magical energy.
The magic within Harry could be influenced by the raw power of the giants. He may be able to access a deeper well of magic due to his exposure to their strength. His spells could be more powerful but also less refined in the beginning. As he enters the wizarding world, he has to learn to control this power better and mold it into the more accepted forms of magic used in Hogwarts.
If Harry Potter was raised by Odin, his magic would take on a whole new dimension. Firstly, his connection to the magical world would be through a very different lens. Odin's knowledge and power are vast, and he would likely train Harry in a much more rigorous and perhaps less structured way than Hogwarts. Harry's magic could be more in tune with nature and the cosmos, as Odin has strong ties to such elements. His ability to communicate with magical creatures might also be different. He could have a more dominant and assertive approach, as Odin's leadership style is quite forceful. His magical skills might not be as refined in the traditional Hogwarts sense, but they would be more adaptable and powerful in a different context.
His magic might develop with a more physical aspect. Since Kushina was a ninja, she might encourage Harry to use his magic in more combat - related ways, like combining spells with physical movements, rather than just relying on the traditional wand - waving.
His magic might develop in a more unorthodox way. The Joker's erratic behavior could lead Harry to use magic in unpredictable situations, which might make his spells more spontaneous but also less controlled.