Harry Potter would likely be one of the main characters affected. Sirius was his godfather, so any changes Sirius makes could have a huge impact on Harry's life, his understanding of his family, and his role in the wizarding world.
In non - lemon fanfiction, their relationship can often be one of mentorship. Sirius, with his experience and knowledge of the wizarding world, could offer guidance to Ginny. For example, he might teach her some advanced spells or give her advice on dealing with the darker aspects of magic.
Well, depending on the context of the fanfiction, Sirius could also be very understanding. If he knew that Harry and Hermione were just having a private conversation about important matters like their fight against Voldemort or schoolwork, he might just give them a knowing smile and say something like 'Carry on, then. Just making sure everything's all right.' He's a rather perceptive character, after all. And he trusts Harry a great deal, so he would likely give them the benefit of the doubt before assuming anything untoward.
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 would probably be very concerned. He might immediately ask her what's wrong and offer her a handkerchief to dry her tears. He has a bit of a wild side, but he also has a big heart, especially when it comes to those he cares about or sees as in need of help.
One popular story might be 'Forbidden Bonds' which explores a unique relationship between them. It delves deep into their characters and how they might interact in a different way than in the original series. The author creates a lot of tension and drama, making it an engaging read.
Often, it begins with Hermione trying to help Sirius deal with his post - Azkaban trauma. She uses her knowledge and compassion to reach out to him. As he heals, he starts to see her in a new light. Their relationship then grows as they start to understand each other better. The lemon parts usually are used to explore their more passionate and private moments, which are often written in a very tender and intense way, adding a new dimension to their relationship.