It could also make Harry more withdrawn. Yelling can be quite intimidating, and Harry might start to keep to himself more, not wanting to draw Snape's ire again. This could potentially affect his relationships with his friends too, as he might be less likely to engage in group activities that could get him in trouble with Snape.
On the other hand, Harry might seek help or advice from other teachers. For instance, he could go to Dumbledore and talk about Snape's behavior. Dumbledore might then give Harry some words of wisdom or even intervene on Harry's behalf, which could lead to a change in the dynamic between Snape and Harry in the fanfic.
Harry might become more determined to prove Snape wrong. He's a stubborn character, and Snape's yelling could fuel his desire to show that he's not the misbehaving student Snape seems to think he is.
Perhaps it's related to Harry's association with his father, James Potter. Snape had a long - standing grudge against James, and seeing Harry might bring back those bitter memories. So, whenever Harry does something that reminds Snape of James, like being overly confident or a bit of a troublemaker, he yells at him.
Snape might initially be taken aback. He's used to students being intimidated by him, so Hermione's outburst could shock him into momentary silence. Then he might retaliate with his usual sarcasm, trying to put her in her place.
One possible reason could be Snape's unfair treatment of Gryffindor students. Hermione, being a strong advocate for justice, might not tolerate his constant bias against her house. She could yell at him when he unjustly deducts points from Gryffindor for minor reasons.
Well, one possible consequence could be detention. Snape is strict and would likely punish Harry for breaking school rules by smoking. He might make Harry clean the Potions classroom or do some other unpleasant chore.
After saving Harry, Snape may have to deal with a lot of mistrust from some people in Hogwarts who don't understand his motives. However, he might also start to form a closer bond with Harry, which could change the whole dynamic between them. This new relationship could lead to some unexpected alliances and enmities within the wizarding world. And if the Dursleys were to try and retaliate, Snape would have to constantly be on guard to protect Harry from any potential harm they could cause.
Mrs Black could be so offended that she starts to plot against Hermione. For example, she might try to get Hermione into trouble with the Hogwarts authorities by spreading false rumors about her.
Perhaps in the fanfic, Snape discovers a powerful and dangerous magic that he wants to use for what he believes is the greater good, but Harry sees it as a threat. Harry has always been wary of Snape, and this new discovery could be the tipping point. Also, if Snape were to make a deal with a dark force in order to gain knowledge to defeat Voldemort but Harry misinterprets his intentions, it could lead to Harry killing Snape.
Snape might be given a warning by Dumbledore at first. Just a simple 'stop this behavior or else' kind of warning.
Snape could be in great danger. Voldemort might immediately try to kill him. Snape would have to fight for his life or try to escape. His status among the Death Eaters would be completely ruined, and he'd become a hunted man.
One possible consequence could be that Harry reveals some deep - hidden secrets. For example, his true feelings about his friends or his fears regarding Voldemort. Since Veritaserum forces the drinker to tell the truth, Harry might disclose information that he has been keeping to himself, which could then change the way Snape views him or the actions he takes in relation to Harry.