One possible plotline could be the revelation of the truth about Harry's parentage and how it affects his relationships with other characters. For example, his relationship with Dumbledore might change as he now has a different family connection through Severus. Another could be how Severus deals with having a son all of a sudden and the challenges he faces in protecting Harry in a different way than he did before.
I'm not sure specifically about 'Wingnat' fanfiction on this topic. But there are many 'Harry is a Severus son' fanfictions out there. You can start by looking on popular fanfiction websites like Fanfiction.net or Archive of Our Own. Some might be really well - written with interesting plot twists and character developments.
A potential plotline could be Severus trying to keep Harry's true parentage a secret from Voldemort. He'd be constantly worried about Voldemort finding out and using Harry against him.
It could also be a more comical plotline. Severus as a pet might constantly be getting into trouble or causing mischief in Hogwarts. Harry is left to clean up the mess and tries to teach Severus (in pet form) some manners. This could lead to a lot of humorous situations, like Severus chasing after magical creatures in the school grounds or getting into battles with other students' pets.
One possible plotline could be that Harry discovers his unique connection to Severus and Lucius and has to deal with the secrecy and the implications within the wizarding world. There might be a lot of internal conflict as he tries to understand his feelings for both of them while also facing the judgment of others.
One plotline could be that Harry discovers a prophecy that ties his future to Severus in a way that leads to them getting secretly married. They then have to navigate through the political intrigue of the wizarding world, with some characters suspecting their relationship and others being completely oblivious. Their relationship grows as they fight against those who would try to break them apart.
One possible plotline could be a magical accident that causes them to be in a situation where they start to see each other in a different light and gradually develop romantic feelings. For example, they might be trapped together in a magically sealed room and forced to confront their feelings.
One possible plotline could be that Harry breaks a major Hogwarts rule, like sneaking into the Forbidden Forest. Snape catches him and decides that a severe punishment is in order, which in this case is spanking. Another could be that Harry fails a very important Potions test repeatedly, and Snape, frustrated with his lack of progress, resorts to this extreme form of discipline. However, these are all just fan - created ideas and not part of the official story.
One possible reason could be Severus' long - standing grudge against James Potter, Harry's father. Since Severus had a very difficult relationship with James, his hatred might be so deep that it clouds his judgment when it comes to Harry, who is a reminder of James. Another reason could be Severus' loyalty to Voldemort in the past. He might fear that accepting Harry as his son could put him in a difficult position with the Death Eaters or those who still hold onto the old Dark Arts ideology.
One interesting plotline could be Harry growing up with Snape's guidance and inheriting his potions skills at an early age. He might have a different dynamic with the other Hogwarts students, being more of an outcast due to his connection to the often - misunderstood Snape.
One possible plotline could be that Harry is raised in the Malfoy Manor. This would give him a very different upbringing compared to his life with the Dursleys. He might be taught different values and magic from a young age.