Harry would likely learn dark magic. Bellatrix is a master of the dark arts, so she would teach Harry curses and hexes that are not typically taught at Hogwarts. He might learn how to use the Cruciatus Curse effectively, for example.
If Harry is raised by Sesshomaru, the magic he learns would be a blend of wizarding magic and something more influenced by Sesshomaru's world. He could learn to use his magic in a more silent and stealthy way, as Sesshomaru is often a silent predator. His magic might also be more attuned to nature, as Sesshomaru has a connection to the natural world in his own realm. Harry might be taught to use magic to create illusions not just for fun but as a serious combat tactic, and he could learn to manipulate his magic in ways that are more fluid and less structured than traditional wizarding magic, allowing for more creative and unexpected attacks.
He would probably learn basic but very powerful defensive magic first. Merlin would know the importance of protecting oneself, so things like a strong Shield Charm or basic protective enchantments would be among the first things Harry learns.
If Harry Potter was raised by Bellatrix, he would likely grow up in a very dark and twisted environment. Bellatrix is a Death Eater, so Harry would be exposed to the dark arts from a young age. His values and beliefs would be very different from the ones he has in the original story. He might not have the same sense of right and wrong, and could be more inclined towards the use of dark magic.
He would probably learn some basic self - defense magic first. Tsunade would want Harry to be able to protect himself, so things like a simple shield charm or a disarming spell would be among the first. Since she is also good at medical techniques in her world, she might also introduce Harry to some basic healing magic early on.
The plot could revolve around Harry's struggle to fit in. Since he is a demigod raised by Bellatrix, he is likely to be an outcast in both the wizarding and demigod communities. The wizarding world may not understand his demigod powers and the demigod world may not accept him because of his connection to Bellatrix. He might have to go on a journey to find others like him or to find a place where he truly belongs. Along the way, he could face many challenges and enemies, both magical and perhaps related to his demigod status.
If Harry was raised by Bellatrix, his character would likely be much darker. Bellatrix is a Death Eater, so Harry would be exposed to dark magic and Voldemort's ideology from a young age. He might be more ruthless and less empathetic compared to the Harry we know. For example, he might not value friendship as highly since Bellatrix doesn't really understand the concept of true friendship. Also, his view of the wizarding world would be skewed towards the pure - blood supremacist ideas that Bellatrix adheres to.
The challenges would be numerous. Socially, he would be an outcast among those who oppose the Dark Arts. His magical education would be limited to Bellatrix's knowledge, which is mainly centered around dark magic. This could put him at a disadvantage when dealing with more complex and positive forms of magic. Emotionally, he would lack the warmth and support that a normal family provides, and this could lead to serious psychological issues.
Harry would likely be more conflicted. With Bellatrix's influence, he might have a darker edge to his personality. He could be more aggressive in his approach to problems. Sirius, on the other hand, would try to keep him on the right path, so there would be an internal struggle. He might not be as quick to trust as the original Harry, but more cautious and calculating.
One possible storyline could be that Bellatrix, despite her dark past, has a change of heart due to some magical influence or a deep - seated love for the Potter family. Sirius, of course, would be a positive influence. They might raise Harry in a more unorthodox way, teaching him both light and dark magic in a balanced way so he can understand the full spectrum. This could lead to Harry being a more powerful and empathetic wizard, able to bridge the gap between different magical factions.
The story would be drastically different. Harry might not oppose Voldemort. He'd be on the 'dark side' instead. His Hogwarts experience would be non - existent or very different if he even went there. He'd probably use the dark arts more often.