Well, in some of these fics, Sirius might time - travel to save Harry from a future threat. For example, he could see a vision of Harry being killed by Voldemort in a new and terrifying way, and then he uses time - turning magic to go back and change the course of events.
Another theme is the power of love. Harry's love for Sirius gives him the strength and courage to face the many obstacles in his way. It's a theme that's often explored in fanfiction as it was also a big part of the original books. In these stories, Harry's love overcomes things like the dark magic surrounding Azkaban or the threats from Voldemort's followers.
One common theme is redemption. Sirius often feels guilty for not being there for Harry earlier, and by saving him from abuse, he is redeeming himself in a way. For example, in many stories, he reflects on how he could have prevented Harry from going to the Dursleys in the first place.
One common theme is sacrifice. Sirius is often willing to put his own life on the line to save Harry. For example, in many fics, he battles powerful dark forces without hesitation to protect the baby.
One great 'sirius saves harry fanfiction' is 'The Guardian's Promise'. In this fic, Sirius goes to extraordinary lengths to protect Harry from various dark threats at Hogwarts. He uses his skills as an Animagus and his knowledge of the wizarding world's secrets to keep Harry out of harm's way.
One great 'Harry Saves Sirius' fanfiction is 'The Rescue Mission' on FanFiction.net. It has a really intense plot where Harry uses his newly learned advanced magic skills to break into Azkaban and free Sirius. The author does a wonderful job of building up the suspense and the relationship between Harry and Sirius.
One popular 'sirius saves abused harry fanfiction' is 'The Bond of Blood'. In this story, Sirius discovers the extent of Harry's abuse at the Dursleys' and takes immediate action to rescue him. He uses his skills as an Animagus to secretly observe Harry and then stages a daring rescue, whisking Harry away to a safe place where he can heal and grow stronger under Sirius' protection.
Another good one is 'Saving Baby Harry: Sirius's Mission'. In this story, Sirius defies all odds to reach Harry. He battles Death Eaters on his way to the Potter's place. Once he has Harry, he flees to a secret location known only to a few. The fic delves deep into Sirius's emotions during this time, from his fear for Harry's life to his determination to keep the baby safe.
Well, in one fanfiction, Harry discovers a hidden spell that can break through the powerful barriers in Azkaban. He secretly practices it and then, with the help of his invisibility cloak, sneaks into Azkaban. He manages to find Sirius who is weak but still has his spirit. Harry uses the spell to free Sirius from his cell and they make a daring escape together, flying out on Buckbeak.
One common theme is family loyalty. Sirius is driven by his love for his brother and his sense of family duty to save Regulus. It shows that no matter how estranged they may seem, family bonds are strong.