When Vader and Leia interact in A New Hope, Vader doesn’t yet know he is her father. In fact, at this point in the story, Vader doesn’t even know his children are alive at all. He assumes, based on what the Emperor told him in Revenge of the Sith, that the child he knew about before turning to the dark side had died along with his wife before she gave birth to Luke.

Sometime between A New Hope and the iconic meeting between Luke and Vader in The Empire Strikes Back, Vader discovers his son is alive. He then embarks on a quest that would ultimately fail: Convincing his son to join him in ruling the galaxy.