One way could be to explore her relationship with Lily before the events of the main series. You could write about their childhood, how their differences started to emerge, and how Petunia felt about Lily's magical abilities at that time.
You could also write a fanfic that delves into Petunia's hidden emotions. Maybe she had some envy towards the wizarding world but was too proud to admit it. By exploring these aspects, you can create an interesting and appropriate 'Harry Potter' fanfic centered around Petunia Dursley.
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.
In a non - offensive and family - friendly fanfic idea, perhaps Petunia Dursley discovers a magical cock cage (not in a vulgar way) that has some connection to the wizarding world. Maybe it was left by a wizard who visited Privet Drive by mistake. Petunia, being the nosy character she is, tries to figure out what it is and how it works. This could lead to a series of comical events as she fumbles with this strange magical object, all while still maintaining her strict, Muggle - like personality.
One possible fanfic could be about Petunia Dursley finding a magical toy that once belonged to Harry Potter's parents. Maybe she discovers it in the attic and it starts to show her memories of Lily and James Potter. She realizes that she has been wrong about Harry all along and decides to change her attitude towards him.
There are indeed appropriate fanfics. Some may center around Petunia Dursley's early life and how it influenced her treatment of Harry. It could be about her jealousy of Lily's magic and how she eventually comes to terms with Harry's presence in her life in a way that is more about family drama and less about anything inappropriate.
One good aspect is the exploration of their family ties. Petunia is Harry's aunt, and despite her coldness, there could be a deeper connection beneath the surface. Another aspect is how Petunia's Muggle perspective clashes with Harry's magical world.
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.
There are fanfictions where Petunia has a change of heart towards Harry. For example, she realizes the error of her ways after seeing how much danger Harry is constantly in at Hogwarts. She then tries to make amends by secretly helping him, like sending him care packages with useful Muggle items that can be adapted for magical use.
In a more comical plot, the lemon could be a mischievous magical object that keeps causing chaos in Petunia's house. It might make things float or turn into strange creatures. Petunia, being the uptight person she is, has to deal with this lemon - induced mayhem while also trying to keep up appearances in front of the neighbors. This could lead to some really funny situations and a change in her attitude towards the strange and magical over time.
Petunia Dursley is significant as she represents the non - magical world's reaction to magic in the Harry Potter series. She is a Muggle who has a complex relationship with the magical world. She has seen magic through her sister but resents it. Her actions towards Harry, like treating him as an outcast in her home, show how some Muggles might fear or be envious of the magical abilities they don't possess.
A possible plot could be a time - travel scenario where Harry and Petunia are sent back in time. They have to rely on each other to survive in the past, and in the process, they learn more about their family history and each other. This shared adventure could lead to a deeper understanding and a different kind of relationship between them.