One great 'Sirius Black back in time' fanfiction is 'Time's Turn'. It has an interesting plot where Sirius goes back and tries to change some key events in the wizarding world. The character development is really well - done, making Sirius seem even more complex and heroic.
One great fanfiction could be 'Sirius's Time-Travel Adventure'. In this fic, Sirius goes back to his school days and tries to prevent certain tragedies. It's really engaging as it shows his interactions with his younger self and his friends. He uses his knowledge from the future to try and change things for the better, and the way the author writes the characters is very true to the original books.
One possible motive could be to save his friends. For example, he might go back in time to prevent James and Lily's death. He was so devastated by their loss in the original timeline, so in the fanfiction, he could use time - travel as a chance to rewrite history and keep them alive.
One common theme is redemption. Sirius often goes back in time to right the wrongs he feels he's committed or to prevent tragedies from happening. For example, he might try to save someone who died in the original timeline.
Well, he might go back in time and try to form stronger alliances. For example, he could seek out Dumbledore at an earlier point and share some crucial information he learned in the future. This could change the course of the fight against Voldemort. Or, he could go back to the time of the Marauders and use his knowledge of the future to create more powerful magical artifacts that could be used against the dark forces. Also, he could go back and try to convince his family to break away from the pure - blood supremacist ideology much earlier, which would have a huge impact on the wizarding world's social structure.
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 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.