During the iconic opening moments of Star Wars: A New Hope, Darth Vader has a tense confrontation with Princess Leia, an adversary who, unknown to him, is actually his daughter. Despite participating in Leia's interrogation, the Sith Lord doesn't uncover his familial connection with the rebellious royal.
She did know she was adopted, as she apparently barely remembers seeing Padme(despite the fact she was only a baby). There's also the fact that Leia was white and both of her parents had tan skin, so it would have been apparent to most that she was adopted.
He found out Leia was his daughter while fighting Luke in episode 6. He read Luke's mind during the fight and discovered that Luke had a sister. He was trying to find a weakness in Luke and discovered that he was worried about the safety of his sister.
Later, the heroes go to the forest moon of Endor to prepare for a battle with the Empire. There, Luke reveals to Leia that she is his twin sister and that Vader is their father.
The Grand Inquisitor (Rupert Friend) was furious with Reva for kidnapping the daughter of an Imperial senator. Reva explained that she discovered a connection between Bail and Obi-Wan in the archives. She doesn't realize that Leia is Vader's daughter.
Why didn't Darth Vader recognise Leia as his daughter in Star Wars: Episode IV? He didn't recognize her because he didn't know his daughter was alive, and he couldn't tell it from reading her mind because she wasn't aware of it herself.
Reva knows that Anakin Skywalker is Darth Vader because she was one of his targets—a child—during the Order 66 killings that took place during the events of Star Wars Episode III: Revenge of the Sith.
In the book 'Tatooine Ghost', Leia learns of Anakin's life prior to his evolution into the Darth Vader personae. This revelation leads her to forgive him. She even named her third child in memory of her father.
Senator Padmé Amidala of the planet Naboo became pregnant during the Clone Wars with her husband, Jedi Knight Anakin Skywalker, as the father. She gave birth to twins, Luke Skywalker and Leia Organa.
In Legends, Luke and Leia do eventually discover their mother's identity during the Swarm War Trilogy.
Assuming that the Empire would try to find the child of Anakin Skywalker, Obi-Wan and Yoda decided that Luke was a prime candidate to be a lure for the Empire, and Leia would be the one trained to fight Vader and the Emperor. At the end of Revenge of the Sith, both children were placed into hiding.
This is not because the Third Sister knows that Leia is Anakin Skywalker's child; it is because the Third Sister found a link between Obi-Wan and Bail Organa and she believed Obi-Wan would do anything to save Bail's daughter.
Leia doesn't get to reunite with Obi-Wan, and instead, just before escaping with Han and Luke, she sees his murder. Of course, Leia doesn't know Darth Vader is her father yet, either in A New Hope and certainly not in Obi-Wan Kenobi. But for the most part, the narrative focus of A New Hope is on Luke.
Theory 1: Leia Doesn't Remember Ben Is Obi-Wan
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan.
She's important in the plot sense because Reva, who is searching for Obi-Wan for Anakin, uses Leia as bait but she's also important because she reminds Ben what he lost in Padmé and Anakin but what he gained in the twins. Leia is just as important as Luke.
She also knows Obi-Wan, and she knows him well. Her holographic plea for help, already iconic, will never be the same. She knows Obi-Wan's real name as well as his alias of “Ben.” When Luke comes barging into her cell and says, “I'm here with Ben Kenobi,” Leia jumps off the bunk in an instant.
However, when they next met in Star Wars: Episode II – Attack of the Clones, Anakin and Padmé's feelings for one another grew into something resembling love, and their wedding at the end of the film solidified their relationship as one of the most important romances in Star Wars history.
The marriage, witnessed by the droids C-3PO and R2-D2, was kept secret due to Amidala's place as a prominent Senator in the Galactic Republic and because of Skywalker's membership in the Jedi Order; the Jedi Code prevented Jedi from falling in love and forming attachments such as marriage.
In Legends material, it is said that the Jedi of old were against the concept of any form of emotional attachment, which means marriage was forbidden.
This is confirmed later in the movie when Obi-Wan informs Padme that Anakin killed them. Both are torn apart with hurt and confusion, trying to make sense of something so terrible.
Did Padme ever cheat on Anakin? No. As explained above, Padme did not cheat on Anakin with either Obi-Wan Kenobi or Rush Clovis.
This time jump makes Padmé a very mature 24 years old, while Anakin is still a Jedi Padawan and teenager at the age of 19. This formidable time in their lives is when the romance between the two sparks, so the age difference between Padmé and Anakin doesn't hold them back.
The Third Sister was at the Jedi Temple during Order 66. She either saw Anakin kill her fellow Jedi or saw the recording of his crimes. That's why she has such hatred for Obi-Wan. She was a Padawan who escaped Order 66.
Haunted by the trauma from her past, the Third Sister sought to exact revenge on the Dark Lord of the Sith Darth Vader for his slaughter of the Jedi during Order 66, which had taken away the only family she had ever known.
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.