Combine turkey, 1 tablespoon beaten egg, water chestnuts, green onion, soy sauce, ginger, black pepper, salt, garlic powder, and red pepper flakes in a bowl.
Use a 3-inch biscuit cutter to cut wonton wrappers into circles. Place 1 1/2 teaspoon of the turkey filling in the center of each wonton wrapper. Brush one side of each wrapper with beaten egg. Fold wrapper over filling, pleating edges as you seal.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C). Fry pot stickers, 6 at a time, until browned, 3 to 6 minutes. Drain on paper towels.
