Vigo never knew who his father was, and in 2358 he and his mother relocated to Camor V where he grew up in her private school. After her murder, Jason pursued a generally directionless life and was arrested several times for minor offenses. Among the problems he had with the authorities was also his fondness for spelunking caves.
In 2370, DaiMon Bok wanted to take revenge on Picard for the loss of his son, who was killed at the Battle of Maxia when his ship was destroyed by the USS Stargazer under the command of Picard. He resequenced Vigo's DNA in order to convince Picard that Vigo was his son. Indeed, after receiving Bok's threat, Picard located Vigo and transported him onboard the USS Enterprise-D. A genetic test convinced both that they are father and son.
Despite the initial difficulties, Picard and Jason bonded. That was when Bok kidnapped Vigo and threatened to kill him. Doctor Beverly Crusher however discovered that he was not Vigo's father because Vigo had Forrester-Trent Syndrome, a condition which is inherited from one's parents, but neither Picard nor Miranda Vigo had the disease. When Crusher further investigated Jason's DNA, she discovered that he was not Picard's son. Picard then transported to Bok's ship and informed him that Vigo was not his son. Once informed of the truth, Bok's associates, who had been told that they would ransom Vigo back to Picard, realized that there was no profit in Bok's actions, and quickly turned on him and released Vigo, who returned to Camor V with the will to get his life in order. As a farewell present, he received a Gorlan prayer stick from Picard and suggested that Picard look him up any time he was in the area. (TNG: "Bloodlines")