One possible fanfiction could be about Aunt Petunia having a strange encounter with a lemon - themed magical object. Maybe she accidentally uses it in a spell (in a non - canon, fan - created way) that makes her see a different side of the wizarding world she has always despised. This could lead to her having a change of heart about Harry Potter and his world.
One possible fanfiction could be about Aunt Petunia discovering her latent witch powers late in life. Maybe she starts having strange dreams that lead her to an old family heirloom that unlocks her magical abilities. She then has to deal with the shock of it all while also trying to keep it a secret from the Muggle world around her.
Well, it could be quite strange. Maybe she's secretly a bit more interested in the wizarding world than she lets on. It might be a way for her to explore the stories from a different perspective, one that's not as judgmental as her usual self towards magic.
Aunt Petunia could discover a lemon tree in her garden that has magical properties. Since she's always been envious of the magical world (even if she doesn't admit it), she might try to use the lemons from the tree to gain some sort of power or advantage. For example, she could think that if she eats the lemons, she'll become more beautiful like the witches she's seen in Harry's pictures.
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.
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.
There are fanfictions where Aunt Petunia has a change of heart towards Harry much earlier in the story. Instead of treating him badly, she starts to secretly teach him some basic things about the wizarding world that she learned from her sister Lily before she passed away. This could add a whole new dynamic to Harry's early years at the Dursleys.
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.
The story could be different in that Aunt Petunia might become more empathetic towards Harry. If she reads fanfiction, she might start to see different interpretations of his situation and understand him better, which could lead to a change in their relationship at home.
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.