In the fanfiction, their relationship would be complex at the start. Snape, having his own demons and secrets, would be a bit of an enigma to Draco. Draco, on the other hand, would be dealing with the loss of his family's status. Snape would start by providing a stable home for Draco. As they interact more, Draco would notice Snape's small acts of kindness. Snape would encourage Draco to explore his own identity outside of the Malfoy name. This would lead to a closer relationship, with Snape teaching Draco about things like loyalty, sacrifice, and the true nature of magic, and Draco in turn bringing out a more human side of Snape.
They would probably become like brothers. With Snape as their common father figure, they would have to learn to get along. Harry might be more forgiving of Draco's past actions, and Draco would have to let go of his animosity towards Harry.
The relationship would be drastically different. Harry, who has always seen Snape as a rather unlikable figure, would start to see him in a new light. He might come to respect Snape as a father figure. Draco, who has some connection to Snape through his family, would now have a more personal and perhaps more positive relationship with Snape. Snape himself would have to soften his usual harsh demeanor towards Harry. And between Harry and Draco, they would be forced to get along better as they are now under the same roof. They might start to understand each other's insecurities and backgrounds more.
The relationship would start off rocky. Snape would be resistant to Harry's kindness as he has always seen Harry as James Potter's son. But Harry's persistent efforts to understand and help Snape would gradually break down Snape's walls.
Well, it often starts with a lot of misunderstandings. Snape has his own preconceived notions about Hermione as a Gryffindor student, and Hermione has her own view of Snape as a strict and often unfair teacher. However, as they live together, small moments start to change their relationship. For example, when Hermione is having trouble with a particularly difficult spell, Snape doesn't scold her but instead patiently guides her. This gradually builds trust between them, and they form a unique bond that is different from the typical student - teacher relationship or even a normal father - daughter relationship.
Well, initially, Harry might be resistant to the idea of being adopted by Snape. He may think it's some sort of trick. But Snape, with his own sense of duty and newfound affection for Harry, tries to break through that resistance. As they spend more time together, Snape might share his own experiences at Hogwarts when he was a student, which helps Harry relate to him. And Harry, in return, might show Snape the good qualities he has inherited from his mother. This exchange of vulnerabilities and shared experiences gradually deepens their relationship into something more like a real father - son relationship.
One possible plot could be that Snape, seeing Draco's vulnerability after the fall of the Malfoy family in the wizarding war, decides to take him in. Snape would then have to deal with Draco's emotional baggage and his own complex feelings towards the boy. He might try to teach Draco a different set of values than what he was brought up with in the Malfoy household.
In such a fanfiction, the plot could involve Snape taking on the role of a father figure to Harry and Draco. He might use his knowledge and skills to protect them from the various threats in the wizarding world. Snape could also teach them advanced magic, which they might not learn otherwise in Hogwarts. And there would likely be a lot of emotional growth for both Harry and Draco as they deal with their new family situation and their past traumas.
At first, it's likely to be tense. Harry has years of seeing Snape as a bully. But as they start living together, they begin to understand each other. Snape might show his more vulnerable side to Harry, like his memories of Harry's mother. Harry, in turn, starts to respect Snape's knowledge and sacrifice. Eventually, they develop a bond like a father - son relationship.
Their relationship develops in a rather interesting way. Snape, being a strict mentor, forces Harry and Draco to look past their differences. Harry begins to understand Snape's past and the reasons for his actions, which in turn makes him more open to Draco. Draco, who has always been in Snape's good graces to some extent, has to adjust to sharing Snape's attention with Harry. This causes some initial jealousy but later leads to a sort of rivalry - turned - friendship as they both grow under Snape's tutelage.
One possible plot could be that Snape, seeing the troubled situations of both Harry and Draco, decides to take them under his wing. He could start by teaching them more advanced magic in a strict but fair way. Harry might initially be resistant as he has his own ideas about Snape, but gradually realizes Snape's good intentions. Draco, on the other hand, might struggle with the idea of being under Snape's authority as he is used to his family's influence. They could all learn to live together, with Snape guiding them through the challenges of Hogwarts and the wizarding world at large.