Well, it could be really strange. Harry might find some new perspectives on his enemies or himself. And Voldemort could get angry as he might not like how he is portrayed in some fanfictions. Maybe he'd try to change things according to what he reads.
In such a fanfiction, Harry might be raised with a very different set of values. Voldemort could try to mold Harry into his own image, perhaps teaching him dark magic. But Harry might also secretly hold on to his own sense of good. For example, he could use the knowledge Voldemort gives him to ultimately turn against him.
In such a fanfiction, Harry might become a very different person. He could be more in tune with the Dark Arts. Maybe he would have a skewed sense of morality, influenced by Voldemort's views. He might also be more powerful in the Dark Arts but struggle with his identity as he is constantly in conflict between what he's been taught by Voldemort and his own inner goodness.
If Harry gives Voldemort the stone in fanfiction, it could be a very dark turn of events. Voldemort would likely use the stone to bring back his physical form more fully or perhaps gain some sort of immortality. However, some fanfictions might explore the idea that this act actually unites the wizarding community against Voldemort in a way that they hadn't been before. They might see Harry's sacrifice as a call to arms and fight back even more fiercely.
If Harry Potter was adopted by Voldemort in fanfiction, it would be a very strange and complex situation. Voldemort is a very evil character, but he might see Harry as a tool or an heir. Harry could be exposed to the darkest magic and the inner workings of the Death Eaters. However, Harry's own strong will and the influence of his parents' sacrifice might still shine through, leading to a possible rebellion against Voldemort later on.
If Voldemort gets custody of Harry in fanfiction, it would be a huge deviation from the original story. Harry would probably be exposed to a lot of dark and cruel things. Voldemort could try to break Harry's spirit and make him abandon his values. There might be a struggle within Harry between the good he has been taught and the evil that Voldemort represents. And the wizarding world would be in even more chaos as Voldemort would have more control over the one person who was seen as the hope to defeat him.
In a fanfic where Voldemort kidnaps Harry, it could lead to a lot of intense situations. Harry might be used as a bait to lure his friends into a trap. Or Voldemort could try to turn Harry to the dark side, using various forms of dark magic and psychological manipulation.
In this kind of fanfiction, one possible scenario is that Harry's whole view of the wizarding world would be warped. Voldemort might try to mold Harry into his own image. He could teach Harry dark magic instead of the traditional magic taught at Hogwarts. Harry might grow up with a completely different set of values and powers, which would surely change the whole dynamic of the fight against good and evil in the wizarding world.
It would be a very strange and dark turn of events. Maybe they would try to rule the wizarding world together in a more 'balanced' way, but it's hard to imagine Harry giving up his values so easily. It could also lead to a completely different kind of magic system emerging as they combine their powers and knowledge.
If they joined Voldemort, the story would go off in a very different direction. Harry might be able to learn more about the Dark Arts directly from Voldemort, which could either corrupt him completely or give him some unique knowledge to use against Voldemort later. Fred and George would likely face a moral struggle. Their loyalty to their family and friends would be tested, and they might try to find ways to protect those on the side of good while seeming to be on Voldemort's side in the fanfiction.
In some fanfictions, if Harry Potter gets broken by Voldemort, it could mean his spirit is crushed. Maybe he loses his will to fight and his friends have to find a way to bring him back. It might involve them using powerful magic or memories to reignite his courage.