Definitely Hagrid. Hagrid has always been around Hogwarts and has a connection to the students. Sirius could interact with Hagrid if he goes back in time. Maybe Hagrid could help Sirius in some way, like providing shelter or information. And Bellatrix Lestrange could also be in the picture. Since she is part of the Black family, Sirius might have to deal with her in the past, either to try to change her or to stop her from doing something evil.
His character may become more cautious. Since he already knows the consequences of his previous actions, he'll be more careful in his decision - making. For example, he might not be as quick to trust Peter Pettigrew again. He could also develop a greater sense of responsibility towards his friends and the wizarding world as a whole, having seen the destruction that Voldemort caused.
One great fanfiction with this plot is 'Time's Redemption'. In it, Harry uses a powerful time - turning spell he discovers in an ancient book. He has to face many challenges in the past, like avoiding detection from the Ministry's time - turner regulations. Another good one is 'Back to Save Sirius'. Here, Harry teams up with Hermione and they use a secret time - travel device left by Dumbledore.
Obviously, Harry Potter and Sirius Black are the main characters. Harry is the time - traveler, and Sirius becomes his mate in this new timeline. Other characters like Dumbledore are likely to also play important roles, as he is always involved in matters related to Harry and the greater good of the wizarding world.
Well, sometimes in these fanfictions, a plot twist might be that Sirius goes back in time and discovers a hidden truth about his family. Maybe he finds out that there was a secret alliance or a hidden enemy within the Black family that was influencing events all along. This could completely change his perception of his family's past and his place in it. Also, he could go back in time and end up being involved in a different kind of magic that was lost in his original time, like an ancient form of magic that has the power to either save or destroy the wizarding world.
There could be unforeseen magical consequences. Time - traveling is a tricky business in the wizarding world. By changing Sirius' fate, Harry might accidentally create new problems. For example, the balance of magic in certain areas could be disrupted. There might also be changes to the Hogwarts' community. Students and teachers who were affected by Sirius' situation in the original timeline might act differently.
One great fanfiction could be where Sirius Black travels back in time to prevent his own imprisonment in Azkaban. He might use his knowledge of the future to avoid being framed by Peter Pettigrew. This could change the entire course of the story, as Harry would then have a more stable and present godfather figure in his life from an earlier stage.
One common theme is redemption. For example, in many fanfictions, Sirius gets a chance to go back and right some of the wrongs he may have felt he committed in his past. Another theme is self - discovery. As he travels through time, he learns more about himself and his place in the wizarding world.
I've read a fanfic called 'Time - Twisted Daughter'. In this story, the daughter's time travel is an accident. She ends up in the past and has to figure out how to get back while also dealing with the chaos of being in a time where her father is still a student at Hogwarts. It's full of mystery and adventure.
One common theme is time - travel. Since there's a 'Time Queen' involved, the stories often play with the idea of Sirius Black traveling through time, either to change the past or to understand the future. Another theme is the power struggle. The Time Queen usually has some sort of powerful abilities related to time, and Sirius might be caught up in a struggle for power or against those who misuse the time - related powers.