Insert a stick into each hot dog, leaving about a 3-inch handle; set aside.
Thread potatoes onto remaining sticks.
Whisk together flour and next 5 ingredients; pour into a tall glass.
Pour peanut oil to a depth of 1 1/2 inches into a large skillet; heat to 350°.
Dip hot dogs in batter, covering well.
Fry hot dogs and potatoes, in batches, 4 to 5 minutes or until golden brown. Serve with mustard or ketchup.
Note: Substitute 1 (8-ounce) package hush puppy mix and 3/4 cup milk or 1 (8 1/2-ounce) package corn muffin mix, 1 large egg, and 1/3 cup milk for flour through vegetable oil.