Stream of consciousness rationale: The important part for answering this question is: Jack does, however, meet Elliot (Michael Angarano), his own biological son, whom he fathered by depositing at a sperm bank as a teenager so that he could buy a leather jacket.
The question and answer pair are described below.
Q: In season three, Jack undertakes a search for his biological father, which ends when he discovers that his father died several years back. Jack does, however, meet Elliot (Michael Angarano), his own biological son, whom he fathered by depositing at a sperm bank as a teenager so that he could buy a leather jacket. He later discovers that the boy's mother Bonnie (Rosie O'Donnell) is a lesbian; she was a nurse at the sperm bank who stole Jack's deposit and was inseminated with it.

Answer this question based on the passage: when did jack have a son on will and grace?
A: In season three