Prepare the ingredients for the batter and filling.
In a mixing bowl, combine the dry ingredients: all-purpose flour, cornstarch, sugar, baking powder, and salt.
In another bowl, whisk together the milk and the egg until well combined.
Gradually add the wet ingredients to the dry mixture, stirring until just combined.
Heat the vegetable oil in a deep pot or fryer to 350°F (175°C).
While the oil is heating, insert skewers into the hot dogs or mozzarella sticks.
Dip each filled skewer into the batter, ensuring an even coating.
Carefully place the battered corn dogs into the hot oil.
Fry for 4-5 minutes, turning occasionally until golden brown.
Remove from oil and drain on paper towels.
Serve with ketchup and mustard on the side.