Yes, there are likely some fanfictions with this concept. Fanfiction writers often come up with creative and alternative family relationships for characters. You can search on popular fanfiction websites like Archive of Our Own or Fanfiction.net using relevant keywords to find such stories.
One common theme is family bonds. Since they are brothers in these fictions, it explores a deeper, more protective family relationship. Another theme is loyalty. Sirius is already known for his loyalty to Harry in the original story, but as brothers, it's intensified. Also, there's often a theme of self - discovery as Harry learns more about his family and himself through this new relationship.
Sure, on Archive of Our Own (AO3), you can discover many 'harry is sirius brother fanfiction'. In these fictions, the authors might rewrite the entire story arc. They could show how Sirius protects Harry in a more brotherly way, and how this new relationship affects Harry's friends and his battles against Voldemort. It's really fascinating to see the different interpretations.
One great fanfiction could be about Sirius Black's brother's hidden life. Maybe he was involved in some secret mission before his untimely death. Writers might explore his relationship with Sirius in more depth, like the times they spent together as children, their shared secrets and how their paths diverged as they grew older.
Archive of Our Own (AO3) is a great place to start. It has a vast collection of fanfictions, and you can use the search bar to type in keywords like 'Harry Sirius brother'. Another option is Fanfiction.net. Just be sure to adjust the search filters to get the most relevant results.
One reason could be Harry's impulsiveness. Harry often jumps into dangerous situations without thinking, and Sirius, being his godfather and having a protective nature, would shout at him to make him realize the risks. For instance, if Harry decides to go after a Death Eater alone.
Sirius could help Harry cope by sharing his own experiences of being an outcast in his family. He could tell Harry that just because his parents did this horrible thing, it doesn't mean he's unlovable. Sirius could also introduce Harry to his friends in the wizarding world, like Remus, who could also offer support and friendship.
It's possible that in the cave, they start to see each other as equals rather than just a mentor - student relationship. They might argue about the best way to deal with the cave's mysteries at first, but through that process, they learn to value each other's perspectives. Also, if one of them gets injured in the cave, the care and concern shown by the other would enhance their relationship.
Yes, there might be such fanfictions out there. Fanfiction writers often come up with creative and sometimes out - of - the - box ideas. They might explore the idea of Harry having a different relationship to Sirius in an alternate universe where he could be seen as Sirius's daughter. However, it's not a common or traditional take on the Harry Potter universe.
The 'Harry Potter' books are set in a magical world full of its own stories, prophecies, and secrets. Sirius is a complex character with a lot on his plate. He has to deal with his family history, his time in Azkaban, and his loyalty to his friends. Fanfiction is a form of creative writing by fans outside the original story. Sirius doesn't have the time or the inclination within the context of the story to be reading fanfiction. His life is too filled with real magical drama and danger.