Place potatoes in a medium-size bowl of cold water. In a separate medium-size mixing bowl, mix together flour, baking powder, salt, and pepper. Stir in the milk and egg; stir until the mixture is smooth. Let mixture stand for 20 minutes.
Preheat the oil in a large pot or electric skillet to 350 degrees F (175 degrees C).
Fry the potatoes in the hot oil until they are tender. Drain them on paper towels
Dredge the fish in the batter, one piece at a time, and place them in the hot oil. Fry until the fish is golden brown. If necessary, increase the heat to maintain the 350 degrees F (175 degrees C) temperature. Drain well on paper towels.