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human
[Star Wars] What would have happened if Vader found out that Leia was his daughter rather than finding out Luke was his son?
gpt
For this to happen, a lot of things need to happen differently.  

Firstly, Vader found out about Luke when he and the Emperor looked into the pilot who'd managed to make the shot that destroyed the Death Star.  From there, it wasn't hard to figure out that Luke was his child, and that Padme had apparently given birth before she'd died.  

So if we're assuming that Vader found out about Leia rather than Luke, how did it happen?  Well, it seems rather unlikely that Leia would ever be in the cockpit of that X-Wing in the Battle of Yavin, so let's look at it from another direction.  Leia was taken to Alderaan to be raised by Bail and Breha Organa.  They managed to keep Leia secret from Vader all these years... but what if they'd failed? What if, somehow, Vader discovered Leia was his daughter while she was still a child?  If that's the case, then Vader would likely personally travel to Alderaan to retrieve her himself.  No doubt Bail and Breha would try to stop him.  No doubt Vader would not take that very well.  There will be blood spilled.  Alderaan's government and populace would object to Vader simply marching into a Prince's home and taking his adopted daughter, possibly killing the Prince and his wife in the process.  This would lead to widespread political and popular unrest against the Empire in Alderaan, which would in turn likely lead to a heavy-handed Imperial response.  

So basically, if Vader discovers Leia's his child while she's still young, then it ends in an Alderaani bloodbath.  

Afterwards, Vader and the Emperor would likely start training Leia in the Dark Side of the Force.  Their success might depend on how young Leia was at the time, the younger the better.  Eventually, Leia becomes a key Darkside assassin and operative for the Empire.  Deprived of such a key politician and negotiator, the Alliance to Restore the Republic never really gets off the ground.  

Next, what if Leia is kept hidden from Vader until after she joins the rebellion.  One of the first key encounters between Vader and Leia took place when he captured her ship, the Tantive IV.  Suppose that Vader senses Leia's Force presence during this encounter, and realizes that she's his daughter.  Well then, Vader would likely take her back to Coruscant and try to turn her to the Dark Side.  Unlike training her as a child, however, the adult Leia proves much more resistant against Vader's teachings.  However, because she never had a Jedi mentor like Luke had Obi-Wan, Leia's resistance is eventually worn down, especially when Alderaan is destroyed by the Death Star.  Leia's spirit is broken, and she submits to the Empire.  In this scenario, Leia still serves the Emperor and Vader, but not as a high-ranking operative.  Instead, her role becomes largely symbolic and political, where she serves as a symbol for rebel-friendly systems abandoning their misguided cause and returning to the embrace of the Empire.  She also uses her Force powers to get a leg up on the other side during negotiations and discussions.  She never receives any combat training, because the Emperor does not trust her.  

Oh, and the Alliance to Restore the Republic *still* doesn't get anywhere, because they've lost one of their most important leaders.