In 'Harry Potter Prisoner' fanfiction, Parvati Patil is an underrated character that could be focused on. She's interested in Divination, and perhaps she has a premonition about the events surrounding Sirius that she initially dismisses. Her sister Padma could also be included, and together they could use their knowledge of different magical studies to help Harry. Additionally, Professor Trelawney could be explored more deeply. She might have some real powers that she's not fully aware of, and in the context of the Prisoner of Azkaban, she could unknowingly give clues that lead to the resolution of the Sirius situation.
Definitely Firenze. He made an appearance in this book, but in fanfiction, he could be more involved. Since he has unique insights as a centaur, he could play a key role in helping Harry understand the prophecies or the true nature of the events related to Sirius. Also, consider Madam Pomfrey. She's often overlooked, but she could be a great source of knowledge about past students and events at Hogwarts that might be relevant to the situation with Sirius.
I think Neville Longbottom is a bit underrated in this book. A fanfic could focus on his growth during this time. He could have some secret knowledge about the plants in the Hogwarts grounds that helped in some way during the events. Also, Seamus Finnigan could be interesting. What if he had some family connection to the events in the Prisoner of Azkaban? Maybe his family knew something about Sirius Black or the Dementors. And Crookshanks is another character. A fanfic could be about his adventures around Hogwarts, and how he was actually more intelligent than people thought and was trying to solve the mystery of Sirius Black himself.
Neville Longbottom is often underrated. In a fanfiction, he could have a more central role within the castle. Maybe he discovers a hidden herb garden in the castle grounds that has magical plants with the power to heal any wound. Another could be Luna Lovegood. She could find a secret room in the castle filled with strange and wonderful magical creatures that only she can communicate with.
One underrated character for Harry Potter OotP fanfiction is Seamus Finnigan. He had his own doubts about Harry in the original story. You could expand on that. What if he had a change of heart in a more in - depth way? Maybe he discovers something that makes him fully trust Harry again. Also, Parvati Patil could be a focus. She could have her own side story about her Divination skills and how they might play a role in the bigger battle against the Dark Lord.
Colin Creevey could be a great character to focus on. He's often seen as just a bit of a fangirl - type character, but in fanfiction, he could have a hidden talent or connection to the Chamber. Maybe he has a family heirloom that gives him some special insight into the secrets of Hogwarts. Another is Myrtle Warren. There's so much more to her story than just being the ghost in the bathroom. She could play a more important role in the events of the Chamber, like having some knowledge that she didn't share in the original story.
Polly Chapman is quite underrated. In fanfiction, you could explore her life more. Maybe she has a secret talent for magic that no one knows about. Another could be Craig Bowker. He could have his own story, perhaps he's involved in some kind of underground magic club at Hogwarts that's not related to the main plot of the cursed child.
Winky the house - elf. She has a lot of potential. In a fanfic, we could explore her life after being freed from the Crouch family. Maybe she has some unique knowledge about the Dark Arts or the Triwizard Tournament that she's been hiding. Her loyalty and her struggle with her new - found freedom could be really interesting to write about.
Argus Filch could be an interesting character to focus on. In fanfiction, we could explore his backstory, like why he is so bitter. Maybe he had a bad experience with magic as a child that made him resentful of the students who can freely use it.
Kreacher. In fanfiction, he could be explored more deeply. He has a complex backstory and a lot of untapped potential. Another one is Queenie Goldstein's sister, Tina. She often gets overshadowed by Queenie in the movies, but in fanfiction, her character could be developed further, especially her Auror skills and her relationship with Newt. And there's also Neville Longbottom's parents. Their story before they were tortured into insanity could be a great focus in fanfiction.
Pettigrew. He's often just seen as the traitor, but in fanfiction, you could explore his motives more. Maybe he was forced into his actions by some dark magic or a threat from Voldemort that no one knew about.
The old hermit character. He was only in a few scenes but seemed to know a lot. Fanfiction could explore his past and how he came to have his knowledge. There's also the young apprentice who was often overlooked. He might have some hidden powers or a special connection to the treasures that could be delved into.