Yes, there are some fanfictions with this concept. It's an interesting take on the Harry Potter universe as it flips the typical relationship between Harry and Voldemort. In these fanfictions, the story often explores how Voldemort's actions change when he takes on the role of an adoptive figure to Harry, who has been abused. It can lead to some really unique character developments and plot twists.
One popular one might be 'Voldemort's New Heir' where Voldemort discovers Harry's abused situation and decides to take him in for his own purposes. He starts to train Harry in dark magic, but an unexpected bond forms between them.
One common trope is the redemption arc of Voldemort. In these fanfics, he goes from being the evil Dark Lord to a more caring figure. Another is Harry's struggle with his past abuse and how he slowly heals with Voldemort's new - found kindness.
Another option is to ask other Harry Potter fanfiction enthusiasts. You could join some Harry Potter - related forums or groups. There are usually experienced readers who have a wide range of knowledge about different types of fanfictions. They might be able to point you in the right direction and tell you about some great stories with this particular plot.
Often, Voldemort starts as this purely evil figure. But when he adopts Harry, he begins to show some unexpected softness. For example, he might start to protect Harry from other threats, which is very different from his usual self.
One possible plotline could be Harry initially being very distrustful of Voldemort, but as time goes on, he starts to see a different side of him. Voldemort, on the other hand, might be trying to use Harry for his own purposes at first but then develops a real bond. Another could be that Voldemort has to face the wizarding world's reaction to his newfound role as Harry's protector, which could lead to conflict. And Harry could grow to become a powerful ally to Voldemort in a new way, changing the power dynamics in the wizarding world.
A possible plot could be that Voldemort adopts Harry after seeing a prophecy that Harry is the key to saving the wizarding world in a different way than just defeating him. So, Voldemort decides to raise Harry in a way that will make him a powerful ally. They go on adventures together, facing ancient magical threats that neither could face alone, and along the way, they form an unlikely bond.
One great fanfiction in this genre is 'A New Beginning' where McGonagall steps in to rescue Harry from his abusive relatives. It beautifully shows how she nurtures him and helps him grow in confidence.
Perhaps Voldemort adopts Hermione with an ulterior motive at first, like using her intelligence to further his own dark plans. But as he spends time with her, he starts to develop a strange sort of paternal feeling. Hermione, on her part, could try to subtly change Voldemort's views. She might introduce him to the value of Muggle - born magic and the importance of equality, which could gradually make Voldemort question his own pure - blood supremacist ideology.
In this fanfiction, Voldemort's character is explored in a way that challenges our traditional view of him. His seeing Harry abused might make him reevaluate his relationship with Harry. He may start to see Harry not just as the Boy Who Lived who he wants to defeat, but as a person who has suffered, much like he might have in his own way. Harry, on the other hand, is stripped of some of his heroic facade. His abuse makes him more relatable in a sense. We can see his pain and how it affects his actions and decisions, and also how he reacts to Voldemort's new - found interest in his situation.