One idea could be that Harry discovers a hidden magic within Azkaban that allows him to free wrongly imprisoned witches and wizards. He then uses this to his advantage to reform the wizarding prison system.
Perhaps in the fanfiction, Harry has to break the rules of Azkaban in order to save his friends who have been unjustly sent there. He might face many challenges like the Dementors and the prison's security spells while doing so. This could lead to a whole new adventure and a change in the relationship between Hogwarts and Azkaban.
One idea could be exploring what would happen if Sirius Black was actually innocent but had a different, more complex plan than just escaping. For example, he might be trying to uncover a deeper conspiracy within the wizarding world that ties to his imprisonment.
One idea could be exploring Sirius Black's life more in depth during his time on the run. Maybe he had some secret encounters with other magical creatures that he never told Harry about.
One idea could be exploring Harry's journey in Azkaban in more depth, like how he copes with the dark and gloomy atmosphere. Maybe he discovers some long - forgotten secrets within the prison walls.
Maybe in this fanfiction, Harry discovers a new kind of magic that allows him to reshape the wizarding world's laws across the globe. He could make Hogwarts - style education available everywhere, even in the remotest Muggle villages. This would not only spread magic knowledge but also bring the two worlds closer together.
For a Harry Potter Azkaban contract fanfiction, perhaps there's a contract between a healer and the Ministry of Magic regarding Azkaban. The healer agrees to try and find a way to lessen the effects of the Dementors on the prisoners, but in return, they want access to some restricted magical knowledge. Or it could be a contract between two prisoners in Azkaban. They make a pact to break out together and seek revenge on those who put them there. They might use their combined magical skills and knowledge of the prison's secrets to plan their escape.
One idea could be exploring Sirius Black's time on the run in more detail. Maybe he had some secret encounters with other magical creatures that he didn't tell Harry about. Another could be a story from the perspective of Remus Lupin during his time as a teacher at Hogwarts that year, and how he was constantly worried about his werewolf secret being exposed while also trying to protect Harry. A third idea could be a fanfic that focuses on Hermione's time - turning device, and what would happen if she accidentally sent herself back too far in time and had to find a way to get back to the right time without disrupting the timeline too much.
In the fanfiction, the female Harry Potter might be sent to Azkaban as part of a plot by Voldemort to get rid of her. While in Azkaban, she discovers a hidden power within herself. It could be related to her connection with her mother or some ancient magic. She then starts to influence the other inmates with her positive energy, and they start to believe in her as a symbol of hope against Voldemort.
In this fanfiction, perhaps a major plot point is Harry using his new position to reform Azkaban. He could introduce new ways of dealing with prisoners that are more humane. Also, his power might attract the attention of dark forces who want to either use him or destroy him, which would add a lot of action and suspense to the story.
A cool plot twist might be that the time - turner Hermione uses has some unforeseen side effects. Instead of just allowing her to attend more classes, it starts to create glitches in time that cause different events from the past to bleed into the present. For instance, old spells from the founders of Hogwarts start to randomly appear in the corridors, and the characters have to figure out how to stop this chaos while also dealing with the Sirius Black situation.
One interesting plot development could be the exploration of Harry's relationship with Sirius Black outside of prison. Maybe they go on adventures together, hunting down remaining Death Eaters. Another could be Harry's improved skills in Defense Against the Dark Arts, as he now has Sirius as a more regular mentor. And perhaps there are new magical creatures introduced that Harry and his friends encounter during their post - Azkaban adventures.