"Ну что ты, право"
"Право" is like "I assure you", "really" here. For example "Право, я не хотел этого" ("I really didn't want it"). This meaning is archaic a little.
"Ну что ты" can be shortage of "Ну что ты (говоришь/думаешь/позволяешь)". In this case it is something like "What are you talking about?" which expresses confusion of the talker: "Oh, stop it! I beg you!".