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 possible plotline could be that Harry discovers a plot against Snape before it's too late. Maybe he overhears some Death Eaters planning to ambush Snape while he's on a solitary mission. Harry then uses his invisibility cloak and magic skills he's learned over the years to outwit the Death Eaters and save Snape. This would show Harry's growth as a wizard and his ability to set aside past differences with Snape.
One possible plotline could be that Harry travels back in time. In this scenario, he stumbles upon a young Severus Snape being bullied by some older kids. Harry, with his knowledge of Snape's future importance and his own sense of justice, steps in to save Snape. This could then lead to a change in their relationship dynamic. Instead of the animosity that exists in the original story, Snape might view Harry in a different light from the start, which could potentially change the whole course of events at Hogwarts in the future.
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.
Another plot could involve the child having special powers or a unique connection to the magical world because of Snape as their father. For example, they might have an extraordinary talent for potions, like Snape, and this draws the attention of both good and bad wizards. It could create a story full of adventure as the child is caught in the middle of different factions vying for their loyalty.
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.
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.