Billy was a mentioned Glader in The Maze Runner. He may have been named after William Shakespeare.
Billy was mentioned when he was ordered alongside Jackson to lock Teresa in the Slammer. He is not mentioned anymore after that and it is unknown if he survived the Maze.
Billy is seen escaping at the end of the first movie, The Maze Runner. It is unknown what happened to him afterwards as he does not appear in Maze Runner: The Scorch Trials.