Vigo never knew who his father was, and his mother decided not to tell him before she died, only that he was in Starfleet. This would instill a mistrust in him about Starfleet for much of his life.
In 2358, he and his mother relocated to Camor V where she started a private school for the orphans there. Jason grew up seeing his mother work tirelessly for the children. However, after his mother's murder in the mid-2360s, Jason pursued a generally directionless life and was arrested several times for minor offenses by the Camorite authorities. This included counts of petty theft, disorderly conduct and trespassing, such as spelunking in the underground cave system.
In 2370, Vigo became involved in a plot by a Ferengi, DaiMon Bok, to exact revenge on Jean-Luc Picard, who killed his son several years prior. Bok secretly resequenced Vigo's DNA so that a genetic test would conclude he was Picard's son. He later found himself transported onto the USS Enterprise-D, where he met Picard. Told his life was in danger, he stayed aboard the ship while the Enterprise crew investigated Bok's location. Despite the initial difficulties, Picard and Jason eventually bonded while they believed they were related.
Doctor Beverly Crusher performed the genetic test, however, she later discovered that Picard was not Vigo's father when she discovered he had Forrester-Trent Syndrome, a condition which is inherited from one's parents. Since neither Picard nor Miranda Vigo had the disease, she further investigated Vigo's DNA and discovered that he was not Picard's son.
The Enterprise found Bok, but, through subspace transporter technology, Bok was able to kidnap Vigo and threatened to kill him. Vigo attempted to bargain with Bok, but he was not receptive. Picard was able to transport in the same way 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.
Vigo 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")