Combine flour, sugar, salt, baking powder, cinnamon. Stir in milk and egg until just combined. Fold in apple. Pour oil into skillet so that it is approximately 1 1/2 deep. Heat oil on high. Oil is ready when a little dough thrown in floats to top. Carefully add dough to oil in heaping teaspoons. Cook until brown, about 2 minutes, then flip. Cook another 1-2 minutes, until both sides are browned. Transfer briefly to paper towels to absorb excess oil, then transfer to cooling rack. Make glaze by stirring milk and powdered sugar together in a small bowl. Drizzle over apple fritters.
Wait approximately 3 minutes for glaze to harden, then flip fritters and drizzle glaze over the other side. Best served warm.