Skewer each hot dog lengthwise and pat dry with a paper towel. This will help the batter stick to the dogs.
Preheat the deep fryer or pot of oil, one inch deep, to 350°F.
In a medium-sized bowl, mix together the flour, cornmeal, sugar, and baking powder.
Add the eggs to the dry ingredients and slowly stir in the milk. Mix until well combined. The batter should be just thicker than pancake batter.
Dip each skewered hot dog into the batter, allowing any excess to drip off.
Transfer the coated hot dogs immediately, in batches of 2, to the deep fryer. Let the skewers rest on the edge of the fryer. Rotate the hot dogs occasionally to ensure even browning.
Cook the corn dogs for 3-5 minutes, or until they are evenly cooked and golden brown.
Once cooked, remove the corn dogs from the fryer and place them on a plate lined with a paper towel to cool and drain any excess oil. Serve and enjoy your homemade fair-style corn dogs!