In 2355, his son was killed in what he called the Battle of Maxia when his ship was destroyed by the USS Stargazer, under the command of Captain Jean-Luc Picard. This greatly affected Bok, to the point that he plotted his revenge for years. He attempted to carry it out in 2364 when he used a thought maker to influence Picard's actions. He tried to trick Picard into taking command of the Stargazer and attacking the USS Enterprise-D, but his plot was foiled. He was subsequently relieved of command of his ship by his first officer Kazago for his "unprofitable venture". (TNG: "The Battle")
After this incident, Bok was stripped of his title of DaiMon and incarcerated at Rog Prison, having been considered unstable and dangerous. He continued planning his revenge and eventually bought his way out of the prison in 2368. Making his way to the Dorias Cluster, he convinced a Ferengi crew that he had regained his title and would lead a profitable ransom mission. However, this was part of the plan, as he resequenced the DNA of Jason Vigo to make it appear on a genetic scan that he was Picard's son. He planned to take revenge on Picard by killing him without a ransom involved. He also gained access to subspace transporter technology to kidnap Vigo and taunt Picard.
In 2370, Bok sent a probe to inform Picard of his plan and Vigo's existence, of which Picard had been unaware. The Enterprise picked up Vigo and trailed Bok to the Dorias Cluster, though it was later discovered that Vigo was actually not his son. Bok successfully kidnapped Vigo, but failed to kill him, prevented by Picard's intervention of using the subspace technology himself. Bok's associates, having learned of the full deceit, apprehended Bok. (TNG: "Bloodlines")
Background information Edit
In the first draft script of TNG: "The Battle", Bok was described thus; "He's smoothly patronizing, clipped in speech, and arrogant. A Beast even Beauty would hate." However, in the final draft of the same teleplay, the latter of those two sentences was omitted. 
In the Star Trek: The Next Generation Companion, author Larry Nemecek said that actor Frank Corsentino couldn't be located to reprise Bok in "Bloodlines", so Lee Arenberg stepped into the role (despite having played another Ferengi, Prak, earlier that season, in "Force of Nature"). Evidently, Corsentino was later "found" and played Gegis in the Star Trek: Voyager episode "Inside Man".
Bok's face, belonging to Frank Corsentino's, was reused for the character of Aramut in the 1995 video game Star Trek: The Next Generation - A Final Unity. Corsentino was not credited in the game, however.
In the Star Trek: The Lost Era novel The Buried Age, Bok's son was named Flax, and the ship he commanded was known as the Seventy-Fifth Rule (referring to the 75th Rule of Acquisition: "Home is where the heart is, but the stars are made of latinum"). The Seventy-Fifth Rule was conducting a survey of the Maxia Zeta star system, discovering a massive wealth of dilithium and other precious metals before the Stargazer arrived in the system on its own survey mission. Believing the Federation to be insane due to its moneyless economy, Flax ambushed the Stargazer, leading to his death in the "Battle of Maxia". Bok arrived in the system afterwards searching for his son's ship, but instead found the abandoned Stargazer and kept it as a personal prize, until he could avenge himself on Picard for his son's death.
In the Pocket TNG novel Indistinguishable from Magic, Bok attempts to prevent the death of his son by using the NX class Intrepid (NX-07) to travel back to before the Battle of Maxia. He enlisted the help of Berlinghoff Rasmussen to achieve this goal. However, he was killed when the Intrepid travelled back to the Big Bang.