Petty (shoulder) has been ruled out of Sunday's game against the Chiefs.
Petty's shoulder injury continued to keep him sidelined through practice this week and will leave him inactive for a third straight game to begin his career. As a result, Geno Smith will serve as the Jets' backup to starting quarterback Ryan Fitzpatrick this Sunday.
McDougle was waived by the Jets on Sunday, Adam Schefter of ESPN reports.
McDougle was originally drafted in the third round of the 2014 draft, but his rookie season was quickly derailed by a torn ACL. The Jets had hoped that McDougle would rebound in 2015, but the 25-year-old never seemed to return to his old self after the injury.
Williams (concussion) will not play in Saturday's preseason game against the Giants.
Even if he were healthy, Williams would face long odds to make the final roster. Matt Forte, Bilal Powell and Khiry Robinson are all locks, and Antone Smith was recently signed to compete for the No. 4 job.
Charles (knee) is not expected to play Sunday against the Jets, according to ESPN's Adam Schefter.
Charles was officially listed as doubtful, so it will not be overly surprising if he misses out. Spencer Ware will likely get the start, with Charcandrick West the backup once again, though the Jets boast one of the better defensive lines in the league, particularly against the run, so a breakout rushing performance is unlikely from either back.