In a medium bowl, whisk together the flour, sugar, baking powder, cinnamon and salt. Add the cider or milk, egg and melted butter and whisk just until combined. Stir in the chopped apple or peach.
In a heavy medium saucepan, heat a couple inches of oil over medium-high heat. When a scrap of bread sizzles when you dip it in, drop a few small spoonfuls of batter at a time into the oil, without crowding the pan. Flip as they turn golden, and continue to cook until golden on the other side. Transfer to paper towels to drain.
Douse in cinnamon sugar or icing sugar while still warm. Makes about 1 1/2 dozen fritters.