In the fanfic world, the author could have given Voldemort a very specific reason for knowing where Harry was. For example, perhaps Voldemort had made a deal with Dumbledore long ago that if Harry was ever in real danger at the Dursleys', he would step in. So when he sensed that danger, he came to rescue Harry. This would add an interesting twist to the story.
Well, in some fanfics, Voldemort might have his Death Eaters spying on the Dursleys. So they could've reported Harry's location to him. Another possibility is that Voldemort has some sort of dark magic tracking device on Harry that led him there.
Maybe Voldemort uses his magic to stun Vernon first. Then he could simply apparate with Harry to a safe place.
Perhaps Voldemort has a change of heart. He realizes that Harry has some value to him alive other than just being his enemy.
In some fanfics, this could happen due to a different take on Voldemort's character. Maybe the author wants to explore a redemption arc for Voldemort. He might see something in Harry that makes him change his mind about killing him and instead decides to rescue him from Vernon's bad treatment. It could also be part of a complex plot where Voldemort has ulterior motives that initially seem like a rescue but are actually part of a bigger scheme.
One motive could be that Voldemort wants Harry on his side. He might think that by rescuing Harry from Vernon, who was clearly a bad caretaker, Harry would be more inclined to listen to him and join him.
One scenario could be that Voldemort has a change of heart. He might have had a vision or a revelation that made him realize that Harry is more valuable alive and not under the cruel treatment of Vernon. Another scenario is that Voldemort wants to manipulate Harry. By rescuing him from Vernon, he can start to build a relationship with Harry based on gratitude. This way, he can later persuade Harry to join his side or use Harry's power for his own purposes.
In some fanfictions, Harry might cope by finding solace in his friends at Hogwarts. He could talk to Hermione and Ron about what Vernon does, and their support gives him strength. For example, they might encourage him to focus on his magic studies as an escape from the Dursley's household.
Obviously, Harry Vernon is a main character. But often, there are other characters created specifically for the fanfic or borrowed from the original source material if it's related to a known franchise. For example, if it's in a magical - themed fanfic, there could be a wise old wizard who guides Harry Vernon on his journey. Or a young sidekick who accompanies him in his adventures.
This is a very disturbing and inappropriate topic. Fanfic should not involve such non - consensual and immoral content. There are many positive and ethical fanfics in the Harry Potter fandom that focus on friendship, adventure, and character growth.
Petunia could be a great addition. Her relationship with both Harry and Vernon adds a lot of complexity. She could be the mediator or the one causing more trouble between them, depending on the plot.
Maybe Vernon is jealous of Harry's magical abilities. He might see Harry as a threat to his 'normal' family image. Also, Vernon has always been a bully at heart and Harry, being an easy target in his house, becomes the victim of his pent - up anger.