Well, for starters, her arrival at Hogwarts would be met with fear and distrust. She would have been taught different values by Voldemort, so she might not value things like friendship and loyalty in the same way. In classes, she could be using her knowledge not for the good of the school or her classmates, but for Voldemort's dark plans. She might also be trying to recruit other students to Voldemort's side during her time at Hogwarts, which would create a very tense and dangerous atmosphere within the school.
Her Hogwarts experience would be extremely different. She might enter Hogwarts as a sort of spy for Voldemort. Instead of being sorted into Gryffindor, Voldemort could have influenced the Sorting Hat to put her in Slytherin. She would be looked at with suspicion by most of the teachers and students who knew of her connection to Voldemort.
She would likely be more guarded and distrustful. Growing up with Voldemort, she would have seen a lot of dark and cruel things. So, she might not be as open and friendly as in the original story. For example, she might not be so quick to trust Harry and Ron when she first meets them.
If Hermione was born a werewolf in the fanfiction, it would transform her Hogwarts journey. She'd constantly be on edge about her secret getting out. Her friendships might be affected too. Ron and Harry might initially be shocked or even a bit scared when they find out. But her intelligence would still shine through. She could be the one to research more about werewolf - friendly magic, maybe even find a way to control her transformations better without relying solely on Wolfsbane Potion. And she'd probably be more involved with the magical creatures aspect of Hogwarts, like the Care of Magical Creatures class, since she has a connection to a creature herself. It would be a very different Hermione at Hogwarts, with a whole new set of struggles and opportunities.
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.
If Hermione was raised by Voldemort in fanfiction, she might have a completely different personality. She could be more ruthless and power - hungry. Her magic might be used for more dark purposes. For example, she could be trained to be one of Voldemort's most powerful lieutenants, using her intelligence to plan his attacks and strategies.
Being raised at Hogwarts would likely make Hermione more confident in her magical abilities from a young age. She would be constantly surrounded by magic and have more opportunities to practice and learn. For example, she might be less hesitant to try out new spells compared to if she had grown up in a Muggle household. Also, her friendships would be different. Growing up at Hogwarts means she forms deeper bonds with her Hogwarts peers earlier on. This could make her more protective of Hogwarts and its traditions as she feels a stronger sense of belonging.
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.
If they joined Voldemort, Harry might lose some of his natural courage. He'd be in a world where his usual values are flipped, and this could make him seem more hesitant. Hermione would probably have to hide her intelligence more. Voldemort doesn't like those who are too smart or independent. So she might act more subservient in public, but in private, she'd be devising plans to break free and expose Voldemort's true nature.
Hermione's academic performance might improve even more. Sirius could provide her with rare books and knowledge from his family's library. For example, there could be ancient spells and magical theories that are not commonly known. This would give her an edge in her classes.
If Hermione transfers to Hogwarts, her relationships would change significantly. For starters, she would have to start from scratch building relationships with her classmates. She might befriend some students who were on the outskirts in the original story. With the teachers, she'd have to prove herself quickly. Some teachers might be more strict with her as a new transfer, while others might be intrigued by her previous magical education. Her relationship with the Gryffindor house as a whole would also be different as she tries to earn her place among them.