One possible fanfic could be 'Petunia's Hidden Affection'. In this fic, Petunia's holding of infant Harry might be a turning point where she starts to feel a strange sense of protectiveness towards him. It could explore her internal struggle between her dislike for magic and her new - found connection to this magical infant.
There might be a fanfic called 'The Moment Petunia Held Harry'. It could show how Petunia's life could have been different if she had embraced Harry instead of resenting him. Her holding of the infant Harry could be the catalyst for a whole new set of relationships and events in the wizarding and non - wizarding world.
She might be feeling a sense of envy. Petunia has always been jealous of Lily's magical abilities, and now seeing Harry, who is also a wizard, could stir up those feelings. She may also feel a bit of fear, not knowing exactly what to do with a magical infant.
In the books, Petunia is rather cold towards Harry from the start. But in the fanfic, the scene of her holding infant Harry might show a more nuanced side. Maybe she shows a moment of hesitation or an unexpected softness that isn't in the books.
A common plotline is the change in Harry's upbringing. Instead of the Dursleys, he could be raised by different characters, like Sirius Black if he hadn't died. Another is the reaction of the wizarding world. People might be more protective of a baby Harry compared to when he was a boy. For example, the Order of the Phoenix could be much more hands - on in his protection.
One idea for a fanfic could be that when Petunia holds infant Harry, she has a premonition of the great things he will do in the wizarding world. This scares her at first, but then she starts to think about how she can be a part of his life in a positive way. It could be a story of redemption for Petunia and a new start for Harry within the Dursley family.
One interesting 'Harry Potter Petunia Dursley' fanfic could be one that explores Petunia's childhood and how her relationship with Lily might have affected her view of Harry. For example, a fanfic could show that deep down, Petunia was always a bit envious of Lily's magical abilities, but also loved her sister in a complicated way. This envy could have then translated into her cold treatment of Harry.
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 are indeed some. However, the quality can vary greatly. Some fanfics might depict Petunia as a more sympathetic single mother, showing how she copes with raising Dudley alone. Others may explore how her knowledge of the wizarding world (even if limited) affects her parenting. It's really a matter of exploring different works to find ones that suit your taste.
Yes, there are quite a few. You can start by looking on popular fanfic websites like Archive of Our Own. Some fanfics might explore a more complex relationship between Harry Potter and Petunia that wasn't fully shown in the original books. They could delve into Petunia's hidden feelings towards Harry, or how their relationship could have developed differently under certain circumstances.
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.
One great fanfic could be 'The Gryffindor's Legacy' where Harry's holding of the flame is a central plot point for him to unlock ancient Gryffindor powers. Another might be 'Flamebearer Harry' which focuses on how he uses the flame to inspire the other Gryffindors in difficult times. There could also be 'Harry and the Flame's Purpose' where he discovers the true meaning of the Gryffindor flame through a series of adventures.