Often in fanfics, Sirius aids Harry in his fight against Voldemort. He could be part of a secret mission to gather information about Voldemort's plans. He may also help Harry find and destroy Horcruxes. Sirius's knowledge of the wizarding world's dark corners and his own courage make him a valuable asset in this fight. For example, he might know of a hidden place where a Horcrux is located or a way to overcome the defenses around it.
In some fanfics, Sirius helps Harry with his relationships. For example, if Harry is having problems with his friends, Sirius can give him advice on how to be a better friend or how to handle conflicts. He can also help Harry when it comes to his romantic interests. Since Sirius was young once, he can offer some wisdom about love and relationships in the wizarding world. Also, if Harry is being bullied by Draco Malfoy or others, Sirius might step in and use his intimidating presence to scare them off.
One common scenario is when Harry is in trouble at Hogwarts. Sirius might break into the school in his animagus form to rescue Harry. Another is when Harry is dealing with the mystery of his parents' death. Sirius can share memories or information that he has about that time, like what really happened the night they died. He can also help Harry deal with the Dementors, as he has his own experiences with them.
One common scenario is during the Triwizard Tournament. Maybe Fleur is struggling with a task, like the second task in the lake. Harry, having already completed it, could give her some tips on how to find the hostages or deal with the merpeople. Another scenario could be when Fleur is facing some form of discrimination or bullying at Hogwarts or in the wizarding world. Harry, being a champion of justice, would step in to support her.
One common scenario is Snape helping Harry with his Potions work. Since Snape is the Potions master, he might offer some extra guidance to Harry, which could be crucial for Harry's progress in school. Another scenario could be Snape protecting Harry from the bullying of other Slytherins. He might not do it in an obvious way, but still intervenes subtly.
One scenario could be that Harry uses his invisibility cloak to help Crane study his patients without being noticed. This would allow Crane to get a more accurate understanding of their behaviors.
Another theme is family. Since Harry lost his parents, Sirius becomes like a surrogate father figure. Fanfics explore how Sirius fills that void in Harry's life, like in some where they celebrate Christmas together in a very family - like way. It gives Harry the sense of a real family that he's been longing for.
In fanfiction, a possible scenario is that Harry Potter, with his ability to understand and manipulate magic, helps Lyanna Stark to unlock some hidden magic within herself. This new - found magic could give her an edge in the political and dangerous environment of Westeros. He could also bring her to Hogwarts for a short while (in the fanfiction world's rules), where she could learn from the professors and gain knowledge that she can apply back in her own land.
One common 'kitty trouble' could be when a magical cat, like Crookshanks, causes mischief in Hogwarts. For example, it might steal potions ingredients from the classroom, leading to chaos as students and teachers try to find them. Another scenario could be a cat getting into a restricted area of the castle and accidentally activating some magical defenses.
One possible scenario could be Sirius noticing how Harry blushes whenever Ginny's name is mentioned. So he might say something like, 'Harry, I've seen you go redder than a Weasley's hair at the mention of Ginny.' Another could be if Ginny gives Harry a special gift, and Sirius teases him about it, 'Harry, that little present from Ginny must mean something special, eh?' A third scenario could be when Ginny is around and Harry acts a bit clumsy. Sirius would then joke, 'Harry, you're more out of sorts than a drunk Hippogriff when Ginny's near.'
Another scenario could be in the hallways. Malfoy might be with his cronies, and they're bullying other students. Harry squints as he decides whether or not to step in and confront Malfoy. It's a moment of decision - should he get involved or let it pass? And the squint is a physical manifestation of his internal debate.
Well, one possibility is that in fanfiction, Death Eaters who survived the war might capture Harry Potter and experiment on him to extract the power of his connection to Voldemort. They might believe that this power could be harnessed for their own evil purposes. Also, there could be fanfictions where rogue wizards from other countries experiment on Harry, seeing him as a unique specimen due to his fame and his defeat of the most powerful dark wizard in history.
Often, in such fanfictions, Sirius may not trust Harry with certain information about his parents or the wizarding world because he believes Harry is too young to handle it. So, he keeps things from Harry, which can lead to conflicts between them. Harry may feel frustrated that Sirius doesn't see him as a capable young wizard, while Sirius is just trying to protect what he sees as Harry's innocence.