She is very much concerned with appearances and normalcy. In the Dursley household, everything has to be in a certain order and conform to what she deems as a proper, non - magical lifestyle. This is part of the reason she is so resentful of Harry and his magical abilities.
One interesting 'Harry Potter Aunt Petunia' fanfic could be the ones that explore her relationship with Lily before she passed away. It might show how they grew up together and how their bond changed over time. Maybe there are fanfics where Aunt Petunia has to face her own insecurities regarding magic and her sister's special abilities.
There could also be other characters from the original Harry Potter series popping up. For instance, Dudley might be in there, and his relationship with both Harry and Aunt Petunia could be explored further in the context of this fanfiction. And of course, depending on the direction of the story, some of Harry's friends from Hogwarts like Ron or Hermione could make an appearance, especially if the story involves the wizarding world interfering with Aunt Petunia's life.
Fanfiction.net is a great place to start. It has a large collection of 'Harry Potter' fanfics, and you can easily search for ones specifically about Aunt Petunia. Just type in 'Aunt Petunia' in the search bar and browse through the results. You might find some real gems there.
Harry initially feels a great deal of resentment towards Aunt Petunia. She has been cruel to him, making him live in a cupboard under the stairs and treating him like an outcast in his own home.
One possible plot line could be Aunt Petunia having a change of heart towards Harry due to some magical event in the fanfiction. Maybe she discovers a hidden side of magic that makes her see Harry in a new light.
One common theme is redemption. Aunt Petunia is often portrayed as having a chance to make up for her years of treating Harry poorly. Another theme is family secrets. There could be secrets about Lily that Aunt Petunia finally reveals to Harry.
One great Petunia fanfiction could be one where she has a moment of self - realization. Maybe she discovers some of Lily's old magic things and starts to understand the wizarding world better. It could show her in a more sympathetic light, perhaps she even tries to protect Harry in her own way.
One interesting 'Harry and Aunt Petunia' fanfiction could be about Aunt Petunia having a change of heart and secretly protecting Harry from other threats in the wizarding world. Maybe she starts to understand the importance of magic and realizes she can't let her sister's son be in constant danger.
By focusing on their shared past traumas. For example, both have had experiences related to Lily's death in different ways. Harry lost his mother, and Petunia lost her sister. They could start to bond over this common pain and gradually move towards a more positive relationship.