Another way could be that Snape uses magic in a unique way. Maybe he casts a small charm that relaxes Harry's nerves. It's not a common spell but something Snape has discovered or created on his own. He might whisper an incantation under his breath while looking at Harry, and soon Harry feels a sense of calm wash over him.
Perhaps Snape would share some of his own past experiences with Harry to make him feel less alone. For example, he could say something about how he overcame difficult situations when he was young, which might give Harry the strength to stop crying. He might say, 'I too faced hardships, Potter, and I did not allow myself to break down like this.'
Snape might simply sit with Harry in silence for a while. Just his presence could be reassuring to Harry. After some time, Snape could start a conversation, asking Harry what is wrong in a more empathetic tone than usual. This gradual approach could help Harry calm down.
Well, in a fanfiction scenario where Snape finds crying Harry, there are so many possibilities. Snape could be secretly pleased that Harry is showing vulnerability, as he has always seen Harry as James Potter's son. But on the other hand, he might also feel a twinge of guilt for how he's treated Harry. The encounter could spark a whole new storyline. For example, Snape could start to protect Harry more secretly, or he could use this as an opportunity to finally have an honest conversation with Harry about their complicated past and present situation.
In some fanfictions, Snape might use his deep knowledge of magic to create a calming spell or potion specifically for Harry. For example, he could brew a special tea with calming herbs that he forces Harry to drink, and as the warm liquid goes down Harry's throat, he starts to feel more at ease.
One possible reason could be remorse. Harry might realize that he misjudged Snape all along. Snape had a complex role, and if Harry discovers the truth about Snape's true loyalties and sacrifices, it could lead to him crying out of guilt for how he treated Snape in the past.
I'm not sure if there is an official fanfiction where Snape specifically finds crying Harry. However, you can start by looking on popular fanfiction websites like Archive of Our Own (AO3). They have a vast collection of Harry Potter fanfictions, and you might be able to find something similar by using relevant tags like 'Snape', 'Harry', and 'emotional' in the search bar.
One common theme is unrequited love. Snape's love for Lily was never fully realized, and this often leads to his emotional breakdowns in fanfiction.
Isolation. Snape is a lonely character. He doesn't have many friends, and he is constantly in a difficult position between the Death Eaters and the Order of the Phoenix. His feeling of being alone and not being fully understood by anyone can lead to crying in fanfiction.
One popular 'Snape crying' fanfiction is 'The Unspoken Pain'. It delves deep into Snape's inner turmoil and the moments that could lead to his crying. The author does a great job of portraying his complex emotions.
One great Severus Snape cries fanfiction is 'The Unspoken Tears'. In this fic, it shows Snape crying after a particularly difficult encounter with the memories of Lily. The author does a wonderful job of delving into his complex emotions.
One popular fanfiction could be 'The Unseen Bond' where Snape stumbles upon fem Harry crying in the Forbidden Forest. In this story, it delves into the complex relationship between them as Snape is initially shocked but then shows a side of unexpected kindness.