Severitus where Severus recognizes abuse in pretty much anyone. He's constantly pulling Slytherins aside to talk about home life, Ravenclaws, even Hufflepuffs, but not him.
He's so desperate for anyone to notice, anyone to actually, truly care, to do something, but that never happens.
Severus assigns a detention and Harry just loses it the second he steps in. Severus makes a single comment, and Harry is completely breaking down. He's shouting, screaming, even better if he's breaking things. Like, absolutely crashing TF out, and then he storms out.
When he shows up to classes the next day, he expects to be practically murdered by Snape, but he's not.
1) An apology letter on his desk, explaining his behavior, demeanor, and offering to help.
2) He gets asked to step out, just like he does with the Slytherins.
3) Normal class period.
4) A hug/reassuring words/just a form of comfort, really.
Severitus where Harry is deeply hurt/affected by Severus' strict/old-fashioned/etc parenting styles.
Severus is always portrayed as strict, sometimes bordering on straight up abusive, but then because he's better than the Dursleys, readers and authors alike tend to agree that it's okay. (IF THAT'S WHAT YOU LIKE, THAT'S FINE SO LONG AS THERE'S A DISCLAIMER.)
But arguably, most often, his tactics are rather harsh. Maybe he's firm on the whole open door policies, or washing mouths out with soap, I've seen a lot with spanking as well, but there's never any after effect, so make there be one.
Oh, he washed his mouth out with soap? Now he's scared to talk.
Spanked? He doesn't see the difference, frankly I don't either, though, so I don't have much to offer here.
No door policy? He feels watched.
Whatever you decide, there should be a point of realization that this is harmful. However that decided though differs.
Make Harry write an essay about Scary Things, and instead of writing about something normal, he writes about how he's terrified of messing up.
Maybe Severus discovers a diary.
Or, and something that I find worked with their personalities, is a massive fight. Harry messed up, and now Severus is threatening whatever, and Harry loses it. "I want to go back to the Dursleys, because at least I know they're cruel, with you it's a mix up."
It's so angsty, om nom nom nom.