Dumbledore might play an important role as well. He would be guiding Harry through this new and strange situation. He could have some secrets about the Lord of Azkaban that he reveals to Harry over time. Also, some of the Azkaban guards or prisoners could become significant characters as Harry tries to reshape Azkaban.
Harry Potter himself is of course very common. He's usually the central figure in these fanfictions. Hermione Granger is also often included as she is Harry's friend and a brilliant witch. Ron Weasley too, as he's part of the trio. Sirius Black might also be a common character since he has a connection to Azkaban.
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.
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.
Maybe he uses some powerful magic spells that he has learned secretly. For example, the Patronus charm could be used to fend off the Dementors which are the main guards in Azkaban. He might also get some unexpected help from his friends or some mysterious characters within the fanfiction world.
It could be Sirius Black. Since he has his own experience with Azkaban, he might know some secrets about the place. He could return in some form within the fanfiction and assist Harry in his escape, maybe by leading him through some hidden tunnels or using some special skills he developed during his time in prison.
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.
Power is a major theme. Harry being in a position of power as Lord Azkaban has to learn how to use it responsibly. Another theme could be redemption, as he might try to redeem the prisoners or himself in some way.
Harry Potter and the Prisoner of Azkaban was a fantasy novel written by K Rowling in England. It told the story of Harry Potter's parents being killed by the evil dark wizard Voldemort. After being adopted by an orphanage, Harry studied magic at Hogwarts School of Witchcraft and Wizardry and defeated Voldemort with his good friend Hermione.
It could be Harry Potter himself, of course. He might be on a mission to either free someone wrongly imprisoned in Caer Azkaban or to stop a new dark threat emerging from there. Hermione could also be a main character, using her intelligence to figure out the mysteries of Caer Azkaban.