Both Snape and Harry stood aghast as the floating ghost of Lily went on: "Oh Severus don't just stare at me, tell him! Tell him of our relationship, how your son came about!"
Snape took a step back. Harry whirled to look at him, at his numb form, feeling the corners of his mouth curl down in horror.
"So it's true? You're my father?" He squeezed his fist around the Resurrection Stone, but it was too small to be painful; it didn't help to distract his stressed mind.
The man's shoulders lowered, he blew out a deep breath. Of course his face remained strained, revulsion twisting his features. Suddenly his eyes caught Harry's with malice.
"No. Were you any less disappointing, I might now acknowledge you as my son-"
"Severus Tobias Snape!" Lily bellowed, quite formidable for a ghost. "I will be having none of that. If there is anyone disappointing at the moment, it's you!"
"Oh quit it, you've said your bit," Snape returned. "I'd rather thought drama was more your sister's game." He advanced on her - Harry wanted to pull him back. "You set me up and you expect me to play along? Do you know how much I hate that son of yours?"
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Edit: I just imagined Snape somehow being able to see Lily's ghost, however that wouldn't be possible I realise with Harry holding the stone. I'd be interested to see a shouting match between the three of them. Interesting point about James, someone saying that if he is not the father, Snape can't hate Harry so much. I just don't think he could change all his years of hatred so fast. This would just irritate him I guess? Oh well, I don't know how he would react to this. Perhaps run quickly in the other direction.
The prompt wasn't really clear, but I meant to show that Snape finds out that he has a son at the same time as Harry does.