Petty was raised in High Point, North Carolina into racing "royalty". The son of Kyle Petty, he was widely expected to become the next great Petty, following in the footsteps of his father, grandfather Richard, and great-grandfather Lee. He was the first known fourth-generation athlete in all of modern American motor sports to participate in the chosen profession of his generations.

Petty began his career in 1998, shortly after he turned 18, in the ARCA RE/MAX Series. Like his father Kyle, he won his first ARCA race, driving the #45 Pontiac at Lowe's Motor Speedway.

Petty moved to NASCAR Busch Series full-time in 1999, driving the #45 Chevrolet. Petty finished sixth in his first Busch Series race at Daytona and had a best finish of fourth place, though he also failed to qualify for three of the Busch races. Petty finished the 1999 season 20th overall in points.

Petty Enterprises planned to have Petty run a second Busch season in 2000, while giving him seven starts in the 2000 NASCAR Winston Cup Series, in preparation for a full Winston Cup campaign in 2001. He struggled early in the Busch season, but managed to qualify in his first attempt at Winston Cup during the DirecTV 500 at Texas Motor Speedway on April 2. He qualified 33rd and ran in the middle of the pack most of the day before his engine expired, forcing him to finish 40th. Adam never got to race alongside his father. Kyle failed to qualify and eventually relieved an ill Elliott Sadler, but Adam was already out of the race. Lee Petty, Adam's great-grandfather, and 3-time NASCAR Champion, lived to see his Winston debut, but died just three days later.

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