The 'Lighter' Side Of The Force
Before getting into the meat of this, let's remember that Vader didn't even know he had children until Palpatine (via hologram) revealed that the son of Skywalker was a threat. At the end of Revenge of the Sith, Palpatine told Vader/Anakin that Padme died of a broken heart and said nothing about the babies, possibly believing they died with her. IF Palpatine had any knowledge that the babies were alive, he would have hidden that from Vader. Fast forward to Return of the Jedi, and I'm reasonably sure Vader knew Leia was his daughter when he died. When Vader told Luke his feelings were strong for his friends and especially his sister, Leia's identity as Luke's sister/Vader's daughter would have been revealed to Vader.
Actually, Vader knew... "The Rebels are there, and I'm sure Skywalker is with them." The opening crawl also explicitly states he was hunting for Luke.He faked his surprised to the Emperor to cover his attempt to convert Luke and overthrow Palpatine.
Actually, Vader hired Boba Fett to hunt Luke, as by that time Vader only knew him by "The rebel that blew the DS-1", Boba Fett finds Luke and fights him, but only gets his name from a friend of Luke's, which used to call him "wormie", Boba Fett reveals this info to Vader, and Vader is hit by Luke's last name. He gets mad at Sidious for not telling him and acts surprised...
Also the fact that when Vader is on the hunt for Luke, he hires DR. Arphra who visits the doctor that assisted Padmé in her labor and death, which reveals the appearance of only one kid, as far as he knew
Here is your definitive answer:As grateful as I am for Lucas bringing Star Wars to all of us, he isn't what I once thought, or what he claims. Referring to Lucas spewing how 'Darth Vader' translates to 'Dark Father', it's nothing but a lie. If we used German AND Dutch to make a SLOPPY translation, maybe. But the fact that Anakin Skywalker and Darth Vader were two separate people until the SECOND draft of Empire means that there was ZERO planning that went into the name 'Darth Vader'. As far as Leia goes, her and Luke weren't brother and sister until Jedi was written. All of this means, we can believe that if Vader sensed Luke had a sister then Vader could also see who this sister was. Aside from that, Vader didn't know before Jedi that he had children, or before Empire that he had a child, because neither did Lucas.
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I believe he knew or sensed that Leia was his daughter as they lowered Han Solo into the chamber (Empiere Strikes Back). Watch the two of them stare at each other as Leia slowly backs into the arms of Chewbacca. Also, during that scene you can see B.Fett raise his towards Chewy and Leia, and Vader quickly twwarted the attempt of B. Fett to fire....just saying
He knew....Read between the lines.