Sift together flour, baking powder, 1/3 cup sugar, and salt. Add milk, egg, and butter; mix with a wooden spoon until smooth.
Drop batter by teaspoonfuls into deep oil heated to 375°. Fry until golden brown, turning once. Drain well.
Combine 1/2 cup sugar and cinnamon; stir well. Roll doughnuts in cinnamon mixture until coated. Serve warm.