Heat 5 inches of oil in a deep-fryer to 365 degrees F. While oil is heating,
Make the batter: In a medium bowl, whisk together the egg and water. Combine the flour, baking powder, salt and pepper; whisk into the egg mixture until smooth. Set aside in the refrigerator.
Assemble sandwiches by placing one slice of turkey on one slice of bread, a slice of ham on another, then sandwich them with the Swiss cheese in the middle. Cut sandwiches into quarters, and secure with toothpicks.
Dip each sandwich quarter in the batter so that all sides are coated. Deep fry in the hot oil until golden brown on all sides. Remove toothpicks and arrange on a serving tray. Dust with confectioners’ sugar just before serving.