Harry's Hogwarts experience would likely be much more political. The Black family has a lot of influence, and there would be those at Hogwarts who would either try to use Harry for that influence or try to undermine him because of it. His time in the Gryffindor common room might be filled with more tension as some students might be jealous of his newfound status. And he might have access to parts of the castle or knowledge that other students don't because of his family connections.
His sorting could be different. Since he's a Black, the Sorting Hat might consider putting him in Slytherin more seriously. His relationships with Slytherin students would be more complex. He might not be as ostracized by them as he was in the original story. Also, his classes could be affected. Teachers who had a bias against the Blacks might treat him differently, while those who were friends with the family could give him special attention.
At Hogwarts, Harry might be seen as a bit of an oddity. His mother being Amelia Bones could mean that he has a reputation to uphold from the start. He could be expected to excel in certain subjects like Defense Against the Dark Arts and History of Magic more than in the original story. His family connections might also lead to some students either trying to befriend him for status or being jealous of him.
His sorting might be different. Maybe the Sorting Hat would consider his Prewett heritage more strongly and he could end up in a different house. He might also have different friends. Instead of Ron and Hermione being his closest allies from the start, he could befriend students from families who were closer to the Prewetts. His classes could be affected too. He might have a natural talent for certain subjects that were more associated with the Prewett family's magical skills.
His Hogwarts experience would likely be very different. He might be more popular right from the start, given the fame of both James and Sirius. The teachers might also have different expectations of him. For example, McGonagall might be more lenient as she had a soft spot for James. And he could have a natural talent for Quidditch, inheriting James' skills. He might also be more involved in secretive activities, like Sirius was, and get into more trouble with Filch.
Her Hogwarts experience would likely be very different. For starters, she might enter Hogwarts with a different reputation. Since she's now associated with the Malfoys, some students might be more wary or even hostile towards her, especially those from families that oppose the Malfoys. Also, she could have access to different resources. Maybe Narcissa gives her special magical items that give her an edge in her studies or in dealing with threats at Hogwarts.
His Hogwarts experience would likely be very different. For one, he might be more physically fit and confident in combat situations. He could be less intimidated by the likes of Snape or Malfoy, as the Dragon Slayer would have taught him to stand up for himself. Also, he might introduce some new skills to Defense Against the Dark Arts, like dragon - slaying techniques adapted for magical creatures.
His Hogwarts experience would be very different. Firstly, he would likely enter Hogwarts with a much higher level of magical knowledge. James and Sirius could have taught him a great deal before he started school. So, he might be ahead in classes like Transfiguration and Defense Against the Dark Arts. Secondly, his social status would be different. Everyone would know he is the son of James Potter, a popular and talented wizard. This could lead to him being more of a center of attention, and he might have a different group of friends. Instead of Ron and Hermione at first, he could befriend students from more well - known wizarding families.
In terms of his relationships, he would have a different family dynamic. He would be more connected to the Black family legacy. This could make him more empathetic towards Slytherins who might also be related to the Blacks. His views on pure - blood and half - blood issues could be more complex. He might also be more likely to explore the darker side of magic in a more controlled way, as he tries to understand his father's past, which would be a significant departure from his original character development.
Harry's personality would change significantly. Narcissa's influence would make him more secretive. He would learn to keep his cards close to his chest. Instead of being the open - hearted hero we know, he'd be more of a behind - the - scenes operator. His relationship with authority figures would also be different. He wouldn't be as quick to trust Dumbledore or other adults. He'd have a more cynical view of the wizarding world's power structures. His social skills would be more attuned to the Slytherin way of networking and manipulation, though he would still have his core of goodness that would lead him to oppose Voldemort in a different, more strategic way.
His classes might be different. The professors might pay extra attention to him, either out of fear or curiosity. For example, in Potions, Snape might be more cautious around him, suspecting he has access to some ancient and powerful potions knowledge from Morgana's side.
Well, he'd probably be more of a legacy student. He might be treated with even more respect or envy from the start. And he could have a different group of friends. Instead of Ron and Hermione, he might be closer to his brother's old gang, like Sirius and Remus, from the very beginning at Hogwarts.