Is Snape actually Harry’s father?
No, Snape is definitely not Harry’s dad. James Potter is Harry’s dad. There is no chance that there is ambiguity or mystery here. Snape was a rival for the affections of Harry’s mom (Lily).
Is Snape related to Harry?
As Rowling explained in a series of tweets, Snape loved Harry’s mother, Lily, and his unrequited affection drove him to resent Harry’s father, James — and by extension, Harry himself.