A possible plotline is that Snape's adoption of Harry causes a rift in the wizarding community. Some might support it, seeing it as a way to keep Harry safe and under the watchful eye of a powerful wizard. Others might oppose it, fearing that Snape's dark past could influence Harry negatively. This conflict could lead to many adventures and challenges for both Snape and Harry as they try to navigate through the political and social turmoil.
One interesting plotline could be Snape initially struggling with his new role as Harry's guardian. He's used to disliking Harry, but as he gets to know him better, he discovers Harry's hidden talents and insecurities. For example, Harry might show an aptitude for potions that Snape had never expected, and Snape has to learn to be a positive influence in Harry's life instead of a critical one.
In some 'Snape Adopts Harry' fanfictions, there is a plotline where Snape and Harry have to work together to uncover a mystery at Hogwarts. This mystery could be related to the Dark Arts or some hidden secrets of the school. Along the way, their relationship evolves from a reluctant guardian - ward relationship to a more loving father - son bond. Harry might start to understand Snape's past actions and Snape, in turn, learns to open up and be more affectionate towards Harry.
A great plotline might be that Snape adopts Harry secretly at first. Harry starts to notice some changes in his life, like getting better study materials and more personal attention in his magical education. As time goes on, Snape has to face his own demons while raising Harry. He might struggle with his past hatred for James Potter while seeing James in Harry. At the same time, Harry could be trying to figure out why Snape is being so nice to him all of a sudden, which could lead to a journey of self - discovery for both of them.
He could develop more patience. Harry, being a curious and sometimes headstrong boy, would test Snape's limits. But as he grows into the role of a father figure, Snape learns to be more patient and understanding, which is a big change from his usually short - tempered self in the original series.
Well, sometimes in these fanfictions, a great plotline is Snape trying to protect Luna from the bullies at Hogwarts. Given Snape's own experiences of being bullied as a child, he would be very determined to make sure Luna doesn't go through the same. He might use his position as a teacher to subtly intimidate the students who pick on her. Also, there could be a plot where Luna starts to teach Snape about the beauty of the natural magic around them. Snape is so focused on the academic and often darker aspects of magic, that Luna's view of the magic in simple things like a butterfly's flight or the way a flower blooms could be eye - opening for him.
One interesting plotline could be Hermione's struggle to adjust to living with Snape. She's used to the warm and inclusive environment of Gryffindor, and Snape's dark and brooding personality makes it a big change for her. Another could be Snape seeing Hermione's potential not just as a student but as a daughter figure, and he starts to teach her advanced magic privately, which in turn helps Hermione to solve some of the school's mysteries.
One common theme is redemption. Snape, who has had a rather dark past in the original series, gets a chance to redeem himself through his relationship with Harry. He can correct the mistakes he made in the past, especially regarding his treatment of Harry.
The concept is popular because it's a fresh take on the relationship between Snape and Harry. In the original series, their relationship is complex and often antagonistic. This idea of Snape adopting Harry flips that on its head and allows for a more positive and nurturing relationship to develop.
In such a fanfiction, the plot could involve Snape taking on the role of a father figure to Harry and Draco. He might use his knowledge and skills to protect them from the various threats in the wizarding world. Snape could also teach them advanced magic, which they might not learn otherwise in Hogwarts. And there would likely be a lot of emotional growth for both Harry and Draco as they deal with their new family situation and their past traumas.
I'm not sure about a specific title, but generally in these types of fan fictions, the story often focuses on how Snape's adoption of Harry changes the course of Harry's life at Hogwarts. For example, Snape might use his knowledge of dark arts and potions to train Harry in a more private and intensive way. This could lead to Harry being better equipped to face Voldemort earlier. Also, the emotional aspect of their relationship, from Snape's initial reluctance to a growing father - like bond, is usually explored in great detail.