Combine flour, baking powder, and salt in a medium mixing bowl; stir well, and set mixture aside.
Combine egg, milk, and shortening in a small mixing bowl; mix well, and stir into dry ingredients. Add clams; stir until smooth.
Drop clam mixture by tablespoonfuls into deep hot oil (375°); cook 3 minutes or until fritters float to the top and are golden brown. Drain well on paper towels.
Transfer fritters to a warm serving platter. Serve immediately with cocktail sauce or tartar sauce.