There could be a fanfiction where both Harry and Sirius accidentally travel to a time during the Marauders' era at Hogwarts. They have to blend in while also trying to figure out how to get back to their own time. This could lead to some hilarious and heart - warming interactions with the young versions of Sirius' friends, like James Potter and Remus Lupin.
In some fanfictions, Sirius Black travels forward in time instead. He gets to see how much Harry has grown and the state of the wizarding world post - Voldemort. It's a great opportunity for him to bond with Harry in a different way, and he might be shocked or proud of how things have turned out.
One interesting story could be where Harry travels back in time and teams up with a young Sirius Black to prevent some of the tragedies that later befall the wizarding world. They might use their combined knowledge of the future and Sirius' skills as an Animagus to outwit dark wizards.
The theme of second chances is also prevalent. In time travel stories, both Harry and Sirius may get opportunities they missed in the original timeline. For example, Sirius could save his friends who died earlier. And also, the exploration of the past and how it shapes the future is a key theme. They go back and learn things that change their perspective on the present and future of the wizarding world.
There's also 'Time's Twist' which delves deep into how time travel affects the relationship between Sirius Black and Harry Potter. The author does a wonderful job of exploring the emotional side of their connection as they navigate through different time periods together. It's full of interesting plot twists and character development.
One interesting fanfiction could be about Sirius Black mentoring Harry Potter in some advanced magic that Dumbledore didn't teach him. It might involve Sirius sharing secrets of the Black family's magical heritage with Harry.
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.
You can start by looking on popular fanfiction websites such as Archive of Our Own (AO3). It has a large collection of Harry Potter fanfictions, and you can easily search for ones that involve Harry and Sirius Black in a time - travel scenario using the search bar.
In some fanfictions, Sirius Black time travels to the past and teams up with his younger self. They work together to expose the Death Eaters' plans earlier. This creates a really cool dynamic as the older Sirius has more experience and the younger one has more energy and impulsiveness.
One common plotline is Sirius Black escaping from Azkaban earlier and secretly training Harry in advanced magic. Another could be Sirius and Harry going on a hidden adventure to uncover more about Harry's parents. There are also stories where Sirius plays a more active role in the fight against Voldemort at Hogwarts, using his knowledge of the Dark Arts and his Animagus form to their advantage.
Often, a common plot point is the struggle against the wizarding world's norms. Since their relationship is rather unconventional in the context of the original story, they face a lot of opposition. For example, in some fanfics, the Ministry of Magic tries to interfere.
There's 'The Unforeseen Bond'. In this fanfiction, the fem Harry Potter's story unfolds in a way that she and Sirius Black are drawn to each other in a rather unexpected manner. It delves into their shared experiences and how they support each other through various challenges.
One interesting fanfiction could be where Harry and Sirius Black's daughter team up to solve a mystery at Hogwarts that the adults are overlooking. They might discover a hidden chamber or a secret about a forgotten spell.