There are indeed. A particular fanfic I read had Snape as a father in a post - war scenario. He tries to rebuild his life and in the process, he adopts a child who lost their parents in the war. It delves into how Snape, with his own troubled past, overcomes his demons to be a good father to this child.
In some fanfictions, Snape is indeed portrayed as Harry Potter's father. Fanfiction allows for creative reinterpretations of the original story, and this is one such interesting deviation from the canon where Snape's complex relationship with Harry takes on a whole new dimension.
A possible plot could involve Hermione inheriting Snape's potions skills in an even more profound way. She could use her combined intelligence from her mother and potions talent from Snape to create new spells or potions. Snape, as her father, would be torn between his loyalty to the Dark Lord (in some versions of the story) and protecting his daughter from the chaos of the wizarding war.
One common theme is redemption. Since Snape had a complex and often dark past in the original series, fanfictions where he is a father often explore his journey of redemption through his relationship with his child. Another theme is protection. Snape is shown protecting his child from various threats, be it from dark wizards or the judgmental wizarding society.
In fanfiction, Severus Snape can be a very complex father figure. He often brings his own experiences of being bullied and his deep knowledge of magic into the role. Some fanfictions show him taking in an orphaned student, for example. He might be strict like he was as a teacher, but with a hidden layer of protectiveness. His actions are often driven by his past traumas and his sense of loyalty, which in a father - figure context means he's dedicated to guiding and shielding the young character.
In some fanfictions, Snape is made out to be Hermione's father. Fanfiction writers often like to play with established relationships and create alternate backstories. This idea might be appealing as it adds a new layer of complexity to both characters' stories. It can lead to different interpretations of Snape's actions towards Hermione in the original series, like perhaps his strictness was a way of protecting his secret daughter in a way.
Harry Potter is often a common character. His relationship with Snape was complex in the original series, and in fanfiction where Snape is a father, it can add another layer of complexity. Harry might be involved in some way, either as an ally or an antagonist to Snape's new - found family situation.
Magic could play a role. There could be a magical spell or potion that was involved in Hermione's conception that links her to Snape. For example, a potion that alters memories and relationships. This would make for a very interesting and complex backstory in the fanfiction. Snape might not even be aware that he is Hermione's father at first, and when he discovers it, his whole view of her would change. He would have to deal with his feelings of protectiveness and his past actions towards her in Hogwarts.
In some fanfictions, Snape's boggart being his father might be due to the abusive nature of their relationship in the original lore. His father was a Muggle who perhaps made Snape's childhood miserable, so it's a deep - seated fear that haunts him even in fan - created stories.