In such a fanfiction, Albus Potter might initially be intimidated by Snape's reputation. But he could gradually discover Snape's hidden qualities. Maybe Snape would become a mentor - like figure to Albus, guiding him in magic that he couldn't learn from others.
Perhaps Snape could help Albus Severus come to terms with his family legacy. Albus Severus is named after two great wizards, Albus Dumbledore and Severus Snape. Snape could share his own experiences of being in the shadow of great names and how to carve out one's own identity in the wizarding world. This encounter could be a very emotional and character - building moment for Albus Severus.
Well, Albus could finally understand Snape's true nature. Maybe he discovers the sacrifices Snape made for his family. He might apologize for any wrong assumptions he had about Snape in the past.
The fanfiction could show Albus Potter learning about the Marauders' values and how they formed their strong bond. He might be in a situation where he needs to form his own group of friends like the Marauders did. The Marauders could also help Albus deal with the pressure of being a Potter. For example, they could tell him how James Potter coped with all the attention he got, and this would give Albus some perspective on his own situation at Hogwarts.
In this fanfiction, Albus Severus might seek advice from Snape's portrait. Maybe Snape's portrait would offer him some wisdom about facing the challenges at Hogwarts, like dealing with the pressure of his name and family legacy.
Snape's reaction would be complex. He has so much history with the Potter family. At the start, he might show his usual cold exterior. However, if Albus shows respect and a genuine desire to learn from him, Snape could gradually warm up. He might share some of his potions knowledge and secrets that he never shared with others. He may also tell Albus stories about his mother, Lily, in a roundabout way, to help Albus understand his family's past better and the sacrifices that were made for him to be alive.
Perhaps James Sirius Potter is on a quest to clear his father's name in some way. He approaches Snape thinking he can get some answers. Snape, on the other hand, has his own grudges and secrets. Their meeting would then be a battle of wits and emotions as they navigate through the past and present issues.
It might be a rather complex relationship. Snape has his own dark past and Albus Severus has the weight of his family name. They could start off on the wrong foot, with misunderstandings, but gradually develop respect for each other as they get to know one another better. For example, Snape might initially misjudge Albus Severus as being just another spoiled Potter, but then realize his determination and intelligence.
In this kind of fanfiction, Snape might be initially very confused and on guard when meeting a Muggle. He could be out of his comfort zone in the wizarding world and struggle to interact with someone who has no knowledge of magic.
In this fanfiction, perhaps Albus Severus Potter would be in awe of seeing his parents. He might have a chance to truly understand their heroic deeds through direct interaction. His parents could offer him advice on how to deal with the challenges he faces at Hogwarts, like the pressure of living up to the Potter name.
He could be injured in a magical experiment. For example, if he was trying to create a new spell with his friends in a secret place, and something went wrong. The spell could backfire and cause him an internal injury. His friends would then be faced with the dilemma of whether to tell the teachers or try to fix it themselves.