Zeus was a busy man. There were lots and lots of gods and demigods that he sired.
If you were Zeus' son or daughter, who would you be? Would you be mortal, like Sarpedon? Would you be immortal, like Helen?
Would you be a god, like Apollo or Dionysus?
How would you deal with Hera's fury? She hates Zeus' illegitimate children. Would you become a great hero, despite her, like Heracles, even if it came at the cost of eternal misery (Heracles was driven mad by Hera many times, and it caused him to murder his wife and children, as well as many other innocent people)?