Well, in this fanfic, it could be that the author delves into the backstory of why Uncle Vernon is so cruel to Harry. It might show how the environment in the Dursley's house affects Harry's growth and development. For example, Harry might become more withdrawn or determined to leave as a result of the beatings. It could also explore the moral implications of such abuse in a magical world where there are laws and a society that seems to be unaware of what's going on in the Muggle - associated part of Harry's life.
Maybe it shows how Harry endures the abuse from Uncle Vernon. It could explore Harry's feelings of helplessness and his thoughts during those tough times.
Hedwig could be one. She might fly off to get help, like to Hermione or Ron. They could then come up with a plan to rescue Harry from the Dursleys.
In this kind of fanfiction, perhaps Harry, out of fear or some form of coercion, starts to obey Uncle Vernon's every order. Maybe Vernon uses threats about expelling Harry from the house or withholding food to make him submit. This could lead to a very different dynamic in the Dursley household, with Harry being more submissive and not showing his usual defiance.
Perhaps Vernon Dursley sells Harry fanfic to get back at the wizarding world that he despises. He might think that by spreading false or embarrassing stories about Harry in fanfic form, he can somehow undermine the reputation of wizards. For example, he could write fanfics where Harry is shown as a bumbling fool, completely different from the real heroic Harry. However, this backfires as the wizarding world sees it as a comical attempt by a Muggle and it actually makes Harry more popular as they rally around to defend him.
Perhaps Vernon is caught up in a wizarding - related incident without realizing it. He might accidentally help some dark wizards thinking they are just normal business partners. When the wizarding world realizes his unwitting involvement, they arrest him to question him about the dark wizards' plans. It could also be that his mistreatment of Harry finally catches up with him in a legal way. For example, if there are laws in the wizarding world about the proper treatment of magical children in non - magical households.
One possible plot could be that Harry has to face his fear of Vernon in a very public and unexpected way. Maybe during a school event at Hogwarts, the boggart appears as Vernon and starts to humiliate Harry in front of his friends and classmates. This would force Harry to confront his past traumas related to living with the Dursleys and Vernon's cruel treatment of him.
In some fanfiction, Uncle Vernon develops by becoming more accepting. For instance, he may start to see Harry not just as a freak but as a person with unique abilities that can be useful. He might begin to tolerate the wizarding world a bit more, especially if he realizes that Harry can use his magic to protect the family from certain threats.
In this fanfic, Harry might get a job as an Auror. He would be involved in solving magical crimes, going on dangerous missions, and working with his old friends to keep the wizarding world safe.
One possible plot could be that Harry shows a special talent early on that Vernon and Petunia recognize as something extraordinary. This makes them see Harry not as a burden but as a valuable part of the family. They then start to love and protect him, and this changes Harry's life completely. He no longer has to endure the abuse and neglect he faced in the original story.
Well, perhaps Vernon might beat Harry out of his extreme dislike for magic. He could be enraged by some accidental magic Harry does at home and lose his temper completely.
One possible plot could be that Harry, through some magical mishap, is transformed into a small animal and Vernon, instead of being his usual cruel self, finds himself oddly attached to this new form of Harry. He might start to protect Harry from other threats in the wizarding world, not fully understanding what he's gotten into but feeling a sense of responsibility.