He didn't know Leia was his daughter. He was only able to get the vague notion from Luke's feelings that he had a twin sister, but not specifically who she was.
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence. "Sister," the Emperor taunted.
Summary. Darth Vader's failure to recognize Leia as his daughter in Star Wars: A New Hope stems from George Lucas's late decision to make Luke and Leia siblings. Leia's Force abilities and her lack of awareness of her true identity also contributed to Vader's inability to sense their familial connection.
Did Leia ever find out Darth Vader was her father?
Alderaan's princess knew she had been adopted by Bail and Breha Organa after the Clone Wars, but she had no idea who her parents were. That was until Luke Skywalker told her the truth - that he was the son of Darth Vader, and that she was his sister.
She was not genetic Organa but still, she is rightful Organa. So yes, Palpatine knew that Leia is daughter of Anakin as well as the fact that Ben is the son of Leia and Han.
Did Vader Sense Leia Was His Daughter in A New Hope? (Legends)
How did Vader know Luke was his son but not Leia?
In canon, Vader found out because Luke told Boba Fett that he was “Luke Skywalker.” This was explained in the canon comic Star Wars (2015) 5. Vader only sensed Leia was Luke's sister because Luke was thinking about her on the Death Star II. When Vader tortu…
No, Anakin was never made aware that he had children until he is initially confronted with Luke, and then suspects between ANH and ESB that Luke is his son. Obi-Wan comments that "the Emporer knew, as I did, that if Anakin were to have any offspring they would be a threat to him.
No. Neither Luke nor Leia found out they were siblings until the third film, Return of the Jedi. Indeed, it wasn't decided that they were siblings until the making of that film (because Lucas no longer wanted to make further sequels about a search for Luke's sister, and decided to wrap everything up with Jedi).
Luke and Leia never sensed that they were twins until Return of the Jedi despite both being sensitive to the Force. Anakin Skywalker's twin children are the original Star Wars trilogy's driving force, having been separated after Padme's death.
Darth Vader acts like he doesn't even know C-3PO or R2D2. They were with him since he was a child. He did everything he could to forget his past. Also, his plating had been replaced many times, and protocol droids all look very similar.
Leia's true family history remained a closely-guarded secret for years, with Leia well aware nobody would trust the daughter of Darth Vader. Marvel's Poe Dameron comic series reveals that Leia actually went to Naboo to learn more about Padmé, trying to get to know her mother through her friends and confidants.
Qui-Gon Jinn believed that the Force itself created Anakin in Shmi's womb, making him the Chosen One who would bring balance to the Force. The revelation confirms that Emperor Palpatine personally manipulated the Dark Side of the Force to create Anakin, making him Anakin's true 'father'.
Yoda. Yoda's knowledge of Luke Skywalker's true parentage was also confirmed in Return of the Jedi. As with Obi-Wan, Yoda believed that Anakin's fall to the dark side made him unsalvageable, with the Darth Vader persona being his only identity following his ascension to Sith Lordship.
Leia was not using the Force or was currently Force-sensitive during her confrontation with Vader. She began training as a Jedi years later. All these reasons prove my point: Vader didn't know Leia was his daughter, and felt no presence of the Force in her, as she was not currently strong with the Force.
He eventually became so desperate to find a way to prevent Padmé from dying that his fear was ultimately the main reason that led to his fall to the dark side. Vader screaming for the loss of Padmé. Even as a Sith Lord, Anakin still loved Padmé very much, but felt great guilt for his actions against her.
As they hide out on Naboo, Anakin sleeps at their house and eats at the family table, all while the family takes a liking to the young Jedi. Padme's mother and sister even tease her about Anakin, encouraging her that they should get together. So, at the very least, they knew about the couple's connection.
Being a master manipulator, Palpatine knew about Anakin and Padmé's secret relationship from the very beginning. It was he who brought them together as adults, manufacturing an assassination attempt that would force the two to reunite.
