When did VADER find out that LUKE was his SON?

When did VADER find out that LUKE was his SON? 1

During the Battle of Yavin, it’s pretty obvious that Vader has no idea that Luke is his son, nor does he sense a familial connection. It’s worth noting that he doesn’t sense one with Princess Leia either, despite being in the same room with her at least three times. The closest he gets with Luke is sensing his Force abilities during the Battle, when he states: “The Force is strong with this one!” But by the beginning of The Empire Strikes Back, he is well aware of Luke Skywalker and knows that he’s a member of the Rebellion, as demonstrated by the scene when his probe discovers the Rebels on Hoth: OZZEL: “My Lord, there are so many uncharted settlements. It could be smugglers, it could be—“ VADER: “That is the system. And I’m sure Skywalker is with them” So, when did Vader find out about Luke? Did the Emperor know that Luke and Leia survived, and kept this from Vader the whole time? Or did Vader and Palpatine both find out the truth sometime after the Battle of Yavin?