One idea could be that Snape discovers a new dark magic plot against Harry early on. He then uses his position as a double agent to mislead the dark wizards while secretly training Harry in advanced defensive magic. For example, he takes Harry to a hidden chamber in Hogwarts at night to practice spells that are not taught in regular classes.
One interesting plot idea could be that Snape raises Harry with a strict but fair hand. He teaches Harry about the Dark Arts not to encourage him to use them, but to make him fully aware of the dangers. Harry might grow up with a more nuanced view of Snape from the start, and their relationship could be a mix of father - son dynamic and teacher - student. For example, Snape could train Harry in potions from a very young age, leading Harry to become a master of potions himself much earlier than in the original story.
Perhaps in the fanfiction, Snape and Harry are forced to team up to defend Hogwarts against a new, unknown dark force. They have to rely on each other's skills and knowledge, with Snape using his potions expertise and Harry his courage and Gryffindor - like bravado. Along the way, Snape shares some of his own experiences with dark magic and how to combat it, making Harry a more well - rounded wizard.
One interesting plot idea could be that Snape, in raising Harry, teaches him advanced potions from a very young age. Harry becomes a prodigy in potions, much to the surprise of the other Hogwarts students. Another idea is that Snape's strict but fair upbringing makes Harry more reserved and less impulsive, which changes the way he interacts with his friends. He might be more cautious and calculating in his actions, especially when dealing with enemies like Voldemort.
One plot idea could be that Dudley somehow gets involved in the wizarding world due to a magical accident. Snape, initially reluctant, has to keep an eye on him. Meanwhile, Harry is caught in the middle, trying to balance his relationship with Dudley and dealing with Snape's grumpiness. For example, Dudley could accidentally drink a potion meant for someone else and start showing magical abilities, leading to chaos and an unlikely alliance between him and Snape to reverse the effects.
One idea could be that during the duel, Harry discovers a hidden spell that Snape was about to use against Voldemort. So instead of a full - on fight, they end up in a truce to discuss this new revelation. This could lead to a whole new understanding between them.
A plot could be that Snape's pet is a phoenix, which is a very rare and powerful magical creature. Harry Potter is intrigued by this phoenix and tries to get closer to it. Snape is initially against this but as the story progresses, he sees that Harry has a pure heart and allows him to interact with the phoenix. This could lead to a bond forming between Harry and Snape through their shared interest in the phoenix.
One plot idea could be Harry struggling to fit in at first in Slytherin because of the house's reputation for dark magic, but then he discovers the true values of loyalty and cunning within it. He could form an unlikely friendship with a pure - blood Slytherin who helps him see that not all in Slytherin are bad. Another idea is that Harry uses his newfound Slytherin traits to outwit Voldemort in a different way than in the original story, perhaps by using more stealth and manipulation.
Perhaps Harry is adopted by a Muggle family who are aware of the wizarding world. They could be a family of scientists who study magic from a scientific perspective. Harry would grow up with a unique understanding of magic, seeing it both as a wonder of the wizarding world and something that can be analyzed. This might make his time at Hogwarts very interesting as he tries to blend these two views of magic.
One idea could be that Harry discovers the truth about his parentage early on. This changes his relationship with Dumbledore as he realizes Dumbledore had been keeping this big secret from him. He might also struggle with his identity, feeling torn between the Gryffindor ideals he was raised with and the Slytherin traits he might inherit from Snape.
A plot could be where a rare and endangered creature chooses Harry and Snape as its protectors. They must travel to different magical locations to find a safe haven for it. This would force them to interact and rely on each other's skills.