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.
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.
Winky the house - elf. She was briefly in the fourth year story but there's so much more that could be done with her. Maybe she has some secrets about the Dark Arts that she's been hiding because she's afraid of getting in trouble.
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.
The house staff could be underrated characters. They've been around the Hawthorne family for a long time and surely know a lot of secrets. Focusing on them could add a whole new layer of intrigue to the story.
Seamus Finnigan could be a great focus. He's often seen as just a side character, but in fanfiction, he could have his own moment. Maybe he discovers a new spell related to the Triwizard Tournament tasks that no one else knows about. He could use this spell to either help Harry or get himself into trouble while trying to prove himself.
Rhonda Kazembe is quite an underrated character. She has a lot of potential for more development. Her skills in various areas could be explored further, like how she might use her knowledge in a different way to help the society in a new situation. Maybe she could be the key to solving a mystery that the others overlook.
Tye Longshadow is often underrated. In fanfiction, he could be given a more central role. His powers are really interesting and his backstory has a lot of potential for exploration. For instance, a fanfiction could focus on his journey to fully master his shadow powers and how he overcomes his insecurities related to being different from the more well - known heroes in the team.
Antoine could be a great character to focus on more. In Sonic SatAM crossover fanfiction, he could have a character arc where he overcomes his cowardice in a new and unique way. Maybe in a crossover with the Archie Sonic comics universe, he could learn some new combat skills from the more battle - hardened characters there.
The servants in the castle, like Lumière and Cogsworth, could be explored more deeply. Their backstories before the curse could be interesting. For example, what were their relationships like? And how did they come to work in the castle?
There's also Grover. He's Percy's best friend, but in a lot of fanfiction, he's just there as a sidekick. He could be developed more, like showing his growth as a satyr and his role in protecting nature. And then there's Clarisse. She's a tough and strong demigod, but often overlooked. Fanfiction could explore her in - depth feelings and her own quests that are separate from Percy's.