One possible plotline could be that it's all a misunderstanding. Maybe Snape was under the influence of a dark spell that made him act out of character and hit Harry. Then the story could revolve around Harry trying to find a way to reverse the spell and save Snape from further disgrace.
In some fanfics, it could be a part of a much larger conflict. For example, Snape might be forced to hit Harry as a way to prove his loyalty to the Death Eaters, but in reality, he's trying to protect Harry in a very convoluted way. He could be playing a double - agent role and this incident is a small part of his grand plan to ultimately defeat Voldemort.
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.
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 finally seeing Harry's potential in potions and secretly mentoring him outside of class. This could lead to a grudging respect between them.
Another plotline is when they are sent back in time together. In these fanfics like 'Back to the Beginning', they have to navigate the past and deal with their past selves. It often leads to some self - discovery for both of them and a chance to rewrite some of their history.
Well, in some fanfictions, Snape might be trapped in a magical trap set by Death Eaters who are still loyal to Voldemort's ideals. Harry, with his natural sense of justice and his loyalty to Hogwarts (where Snape also has a complex connection), figures out the trap's mechanism and manages to free Snape. Or perhaps Snape is on the verge of being attacked by a magical creature, and Harry, using his experience with magical creatures from Hagrid's teachings, scares the creature away and saves Snape.
One plotline could be that Snape and McGonagall discover a hidden threat against Harry early on. They decide to secretly train Harry in advanced magic that neither Voldemort nor his Death Eaters know about. Snape might use his knowledge of the Dark Arts to teach Harry how to counter the most dangerous curses, while McGonagall focuses on strengthening Harry's Transfiguration skills to help him in combat and escape situations.
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.
One interesting plotline could be Snape realizing that Harry is not like the 'Boy Who Lived' (WBWL) as everyone expected. Maybe Harry has a different approach to magic that Snape initially scoffs at but later comes to respect. For example, Harry might be more interested in the darker arts in a way that challenges Snape's views.
Well, a common plotline is that Snape is initially reluctant to be around baby Harry due to his hatred for James. But as he spends time with the baby, he starts to see Lily in Harry. He might start to protect Harry not just for Lily's sake, but also because he begins to care for the child himself. Some fanfictions also explore how Snape's interactions with baby Harry might change the future events in the wizarding world, like how it could affect Harry's relationship with Snape when he grows up.
Well, a popular plotline is the redemption of Snape through his relationship with Harry. In these fanfictions, Harry gradually discovers the sacrifices Snape has made for him and the wizarding world. This leads to a new - found understanding and even a form of friendship between them. There are also fanfictions that explore what would happen if Snape adopted Harry, which is a very different take on their relationship.