Snape would probably be very conflicted. On one hand, he has a long - standing grudge against James Potter, Harry's father. But on the other hand, he loved Harry's mother, Lily. So, he might be cold at first, but then his sense of protecting Lily's son could kick in. He would likely be very strict with Harry, as he is with all his students, but also secretly keep an eye on him to make sure he's safe.
One common theme is his difficult childhood. Many fanfictions explore how his family situation, like his relationship with his father, affected him. Another theme is his early days at Hogwarts, including his friendships and rivalries, especially with the Marauders. Also, his budding interest in potions and dark magic is often a theme.
There is also 'A Childhood with Snape and Lily'. It details their adventures in the wizarding world as children. It's full of little magical moments that they shared, like exploring the Forbidden Forest together (although they weren't really supposed to) and their first attempts at magic outside of school lessons. It really gives a vivid picture of their early relationship.
One interesting Hermione and young Snape fanfiction could be 'Time's Anomaly'. In it, Hermione accidentally travels back in time and meets a young Snape. Their interactions are filled with tension as Hermione tries to understand the roots of Snape's complex personality. Another good one is 'A Different Perspective' where Hermione is tasked with mentoring young Snape in a magically - altered Hogwarts scenario. It's fascinating to see how their relationship develops despite their age and background differences.
One common theme is unrequited love. Snape has deep feelings for Lily, but she often just sees him as a friend. Another theme is the power of friendship in their early years. They start off as friends and that friendship is a big part of their story in these fanfictions.
Friendship is another theme that can be intertwined. His friends' reactions or lack thereof to his situation can be a major part of the story. Some fanfictions also explore the theme of acceptance, not just from others but also self - acceptance. How Snape learns to accept himself and his feelings in a world full of norms and expectations is often explored in great detail in these fanfictions.
Common themes in young Severus Snape fanfiction are his search for identity. As a young wizard, he was trying to figure out who he was, especially in a world that wasn't always kind to him. Another is his love for knowledge. His constant pursuit of learning more about magic, whether it was dark or light magic, is often a central part of these fanfictions. Also, the theme of loyalty. We see his loyalty to certain people or ideals start to form at a young age, which later becomes a major part of his character.
One popular young Snape fanfiction is 'The Prince's Tale: Snape's Early Years'. It delves into his childhood, his relationship with his parents, and how those experiences shaped him into the person we see in the Harry Potter series. Another is 'Young Snape and the Hogwarts Mysteries' which focuses on his time as a student at Hogwarts, his friendships, and rivalries.
I really liked 'Snape's Time - Twisted Fate'. Here, Snape's time travel leads to some unexpected alliances. He teams up with some characters he previously had issues with, and together they try to prevent a major disaster from happening. The story is full of twists and turns, and the way the author weaves the time travel elements with the existing wizarding world lore is quite impressive.
You can try fanfiction.net. It has a large collection of various fanfictions, including those related to young Harry and Snape. Just use the search bar and type in relevant keywords like 'young Harry Snape' and you'll likely find many stories to choose from.