Did Joseph Kennedy jr have children?

Yes, he had three.

A daughter, Caroline Kennedy, born November 27, 1957. She expressed an interested in being appointed to Clinton's vacant Senate seat from New York. (After Senator Hilary Clinton was appointed as the current Secretary of State, her Senate seat was vacant.)

A son, John F. Kennedy, Jr. born November 25, 1960, and died in a self piloted airplane crash on July 16, 1999; killing himself, his wife and his wife's sister (his sister-in law).

A son, Patrick Bouvier Kennedy, born August 7, 1963, died August 9, 1963. He was born 5 1/2 weeks early, by emergency Cesarean delivery. He was just 4 pounds 10 1/2 ounces, and ultimately died of RDS or Respiratory Distress Syndrome.