He might have a very nurturing relationship. Since he had a tough life himself, he'd want to make sure his grandchildren are happy. He could be strict when it comes to their magical education but also very loving.
Well, in this fanfiction, perhaps Snape would be initially shocked. He might see his own traits in his grandchildren. He could share his knowledge of potions or magic with them in a more gentle way than he ever did with his students. Maybe he would tell them stories about the old days at Hogwarts, including his time with Harry Potter and the other characters.
In fanfiction, when Aang meets his grandchildren, it could be a very heartwarming moment. He might pass on his wisdom about airbending and the importance of balance in the world. Maybe he'll tell them stories of his adventures with his friends, like how they defeated the Fire Lord and brought peace to the four nations.
In fanfiction, when Darth Vader meets his grandchildren, there could be a moment of shock and confusion. His dark past might contrast sharply with the innocence of his grandchildren. Maybe he would initially be feared by them, but as time passes, he could show a side of him that was long buried under the Vader persona, a side that is capable of love and protection.
Perhaps it would start off rocky. His grandchildren would be wary of him because of his reputation. But as they get to know him, they realize he has changed and they start to form a bond. They might learn from his experiences and he from their fresh perspectives on life. It could be a relationship of mutual growth.
Perhaps Snape would initially mistake the Dursleys for some sort of Muggles with a bit of dark magic in them due to their cruel nature. He could start investigating them, which would cause chaos in the Dursley household as they try to hide their secrets from a wizard like Snape.
In a fanfiction where Snape meets the Avengers, it might start with a lot of confusion. Snape is from a world of magic and the Avengers are from a world of superpowers. Snape could use his potions skills to create something that might give the Avengers an edge in a battle. For example, a potion that could temporarily enhance their powers. However, his sarcastic and often untrusting attitude might make it difficult for him to fully integrate with the team at first.
One possibility could be that Snape meets James Sirius Potter in a Hogwarts flashback scenario. Maybe James Sirius Potter discovers some old memories or secrets related to Snape through a magical object. This could lead to a whole new understanding of Snape's character for him.
One idea could be that Hermione accidentally travels back in time and meets a younger Severus Snape. She could initially be shocked by his younger appearance and different demeanor. Maybe she tries to help him with his studies or deal with the bullies in his life, which would create an interesting dynamic as she already knows his future self.