Vader might initially be shocked. His son reaching out to him is unexpected. He could respond with a moment of silence, trying to process what is happening.
Luke's meeting with Vader in the comics occurs when Luke stumbles upon a secret operation by Vader. Their interaction leads to a showdown that has significant implications for the story.
This would be a huge twist. It might mean Luke is seduced by the dark side's power or has some ulterior motive for joining Vader. It could change the course of the entire story.
Well, it could be a fanfiction where Luke and Vader have an unexpected relationship, perhaps a more tender or different take on their usual dynamic, like Vader showing a soft side towards Luke as if he were a little baby in terms of being protective or having some newfound paternal feelings. But without reading it, it's hard to say exactly.
In some fanfiction, if Luke and Darth Vader teamed up, they could be an unstoppable force for good. They could use their combined Force abilities to fight against a greater evil in the galaxy. Maybe they would start by taking on the Emperor together, using Vader's knowledge of the Sith and Luke's purity in the Force.
Well, it could also lead to a secret meeting between them. Luke's call might prompt Vader to arrange a discreet encounter where they can talk more freely. During this meeting, Luke could try to persuade Vader to turn back to the light side, and Vader might be more receptive than expected because of that initial call. He might share some of his inner turmoil and regrets with Luke.
If Darth Vader raised Luke and Leia, Luke could be more introverted. He'd have to constantly grapple with the knowledge of his father's actions and his own potential for darkness. His training would be intense, and he might be less likely to trust others easily. Leia would be a more complex character. She would have a love - hate relationship with Vader. On one hand, he's her father, but on the other, he represents everything she hates about the Empire. This would make her personality more unpredictable, sometimes showing compassion towards Vader and other times being extremely hostile.
You could try searching on popular fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. Just type in the title 'luke vader my little baby' in their search bars and see if it pops up.
His view could become more complex. Before, Vader was mainly an enemy. But seeing his fall, Luke might start to see him more as a tragic figure, a victim of the dark side's power.