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.
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.
Obviously, Luke Skywalker and Darth Vader are the main characters. Luke, the heroic Jedi, and Vader, the complex Sith Lord. In this fanfiction concept, their relationship is likely to be re - imagined in a very different way compared to the original Star Wars story.
One possible plot could be that Luke discovers he has a special connection with Vader that goes beyond their typical relationship in the Star Wars universe. Maybe he starts having dreams where Vader is trying to teach him a new form of the Force, something that was lost to the Jedi. And as Luke delves deeper into these dreams, he begins to understand Vader in a more empathetic way.
The little angel could start off as a mysterious and seemingly innocent being. As the story progresses, it could be revealed that it has a much deeper knowledge of the Force and the history of the Skywalker family. For example, it might know secrets about Anakin Skywalker's fall that no one else does.
One idea could be that Luke discovers a young Force - sensitive 'little angel' figure who has a connection to Vader's past. Maybe this little angel was a symbol of hope on Vader's home planet long ago. Luke then tries to protect the little angel from the remnants of the Empire who want to use its power for evil.
Their relationship could develop uniquely if Darth Vader starts to have dreams about Baby Luke's future as a great Jedi. These dreams make him question his loyalty to the dark side. So he begins to secretly guide Luke in the ways of the Force, like leaving behind ancient Jedi texts for the baby to find when he's older.
A great plot idea could be that Darth Vader is ordered by the Emperor to kill Baby Luke, but he can't bring himself to do it. Instead, he fakes the baby's death and takes him to a hidden Jedi enclave. There, with the help of some remaining Jedi, they start to train Luke in secret. Meanwhile, Vader has to constantly deceive the Emperor about Luke's whereabouts and his own actions regarding the boy. This would create a lot of tension and drama in the fanfiction as Vader is walking a very dangerous line between the dark side and a newfound sense of hope through the baby.
One common theme is redemption. Vader's journey towards redemption through his connection with Luke is often explored. It shows how love for his son can make him turn away from the dark side.
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.