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.
One possible plot could be Harry growing up believing he is on the right side by following Bellatrix and the Death Eaters. But then he discovers some secrets about his real parents and starts to question everything he's been taught. This leads to an internal struggle as he tries to decide whether to stay with Bellatrix or break away and find his true identity.
One possible plot twist could be that Harry, under Bellatrix's influence, becomes a much darker and more ruthless wizard. Bellatrix might train him in the Dark Arts, and he could end up being a sort of anti - hero. He might have a completely different view of the wizarding world and be at odds with his former friends from Hogwarts.
Well, for one thing, his view of the wizarding world would be completely different. Growing up with Bellatrix, he'd probably be taught that pure - blood supremacy was the right way. His relationships would also be altered. He might not have the same friends like Ron and Hermione. Instead, he could be surrounded by Death Eaters or those with dark leanings. His magical skills might develop in a more aggressive and unethical direction as Bellatrix would encourage using magic for domination rather than for good.
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.
One great Bellatrix fanfic is 'The Redemption of Bellatrix'. It shows a different side of her, exploring the possibility of her having a change of heart. It's really interesting to see how the author weaves a new story around her character.
In a time - travel Bellatrix fanfic, she might go back to the time when she was first introduced to the Dark Arts. This could show a different side of her, perhaps a more innocent - looking but still dark - inclined Bellatrix. She could interact with younger versions of other Death Eaters and form different alliances that change the course of the future in the wizarding world.
One great 'Harry Potter x Bellatrix fanfic' is 'The Unlikely Bond'. It explores a very different relationship dynamic between Harry and Bellatrix. It shows how Harry, in this fictional scenario, tries to understand Bellatrix's twisted mind and in the process, they develop a strange connection that is full of tension and mystery.
Harry could become more secretive and distrustful. Growing up with Bellatrix, who is part of the Death Eaters and has a lot of secrets, Harry would learn to keep things to himself. He may not trust others easily, even those who seem friendly, as he has been brought up in an environment full of lies and hidden agendas.
Harry might be more secretive. He'd have to hide any doubts or conflicting feelings he has about the dark path he's being led down. Bellatrix would not tolerate any signs of weakness or deviation from her plans. So, he'd become very good at hiding his true self, which would make his personality complex and full of contradictions.