Do reptiles have three classes

No. Reptiles are a single class. There are four orders of reptiles, one of which is not well-known. The well-known orders are Testudines (turtles and tortoises), Crocodilia (crocodiles, alligators, and gharials), and Squamata (lizards and snakes). The fourth order is Rhynchocephalia, which consists of only two species native to New Zealand known collectively as the tuatara.