Well, perhaps the child in the 'Harry Potter child in Azkaban' fanfiction forms unexpected alliances. Maybe they team up with some of the inmates who have their own reasons to oppose the unjust system of Azkaban. This could lead to a series of adventures where they try to break free from Azkaban's clutches together.
One interesting plotline could be the exploration of how the vampire element changes the dynamics in Hogwarts. For example, it might create new alliances or rivalries among the students. Maybe the vampire character has unique powers that influence the outcome of certain events, like the Quidditch matches.
One possible plotline could be Harry's attempts to prove his innocence while in Azkaban. He might use his magical skills in unexpected ways to communicate with the outside world and gather evidence.
One possible interesting plotline could be the Rose Child having unique magical abilities that are different from the regular magic in the Harry Potter world. For example, they might be able to communicate with a special kind of magical creature that others can't.
Obviously, the child is one of the main characters. There might also be some prison guards who play important roles, either as antagonists or those who gradually change their views towards the child. And perhaps some other inmates who interact with the child could also be considered main characters.
One possible plotline could be that Harry is wrongly accused and sent to Azkaban. While there, the Dementors constantly torture him with their presence, draining his happiness and hope. Another could be that a dark wizard within Azkaban has a vendetta against Harry and uses dark magic to physically and mentally torture him. Or perhaps the prison system itself, with its harsh conditions and lack of proper care, is a form of torture for Harry, and he has to find a way to endure and escape while dealing with the psychological trauma.
One interesting plot could be a new adventure where Harry discovers a hidden chamber in Azkaban that holds a powerful magical artifact. This artifact might be related to an ancient wizarding family and its secrets. Another plot could involve the Dementors having a different origin than what is known in the original series, and Harry has to find a way to stop them from spreading a new kind of dark magic.
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.
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 interesting 'Harry Potter and Azkaban' fanfiction could be about Harry exploring more of the secrets within Azkaban before his third year. Maybe he discovers a hidden passage that leads to an ancient wizarding artifact. Another could be a story where Sirius Black has an entirely different plan while on the run from Azkaban, one that involves helping other wrongly imprisoned wizards escape. And there are fanfictions that focus on the Dementors' origin and how it relates to Azkaban, like a theory that they were created by a dark wizard who once ruled the prison island.
Perhaps a plotline where Harry discovers other immortal beings. He could form a sort of community with them, learning about different cultures and powers that immortality has bestowed upon them. They might teach him how to better control his immortality, like hiding his true nature from mortals or using his extended lifespan to gain knowledge that no one else has. This could lead to adventures as they try to protect their secret from those who would seek to exploit it.