In a medium bowl, combine cornmeal, flour, salt, pepper, sugar, and baking powder. In a separate bowl, gently whisk the eggs with the milk and stir into the dry mix.
Preheat the oil in a Dutch oven, deep saucepot or mini fryer to 350 degrees F.
Insert wooden skewers through the center of each frankfurter.
Dry frankfurters with a towel, then dust with cornstarch and shake off the excess. Then hold the frankfurters by the end of the skewer and dip in the batter until well coated. Let the excess batter drip off.
Carefully holding the end of the skewer, let the corn dogs fry for 5 seconds before letting go to prevent them sticking to the bottom of the pot. Fry until lightly browned, about 3 minutes. Drain on paper towels.