Pour oil into a deep-fryer or cast-iron Duth oven fitted with a candy/fry thermometer and heat to 375ºF.
Combine the cornmeal, flour, salt, baking powder, baking soda, and cayenne pepper in a medium mixing bowl. In another bowl, combine the jalapeno, corn, onion, and buttermilk. Add the dry ingredients to the wet ingredients all at once, and stir only enough times to bring the batter together; there should be lumps. Set the batter aside to rest for 10 minutes.
Scatter the cornstarch onto a dry plate. Roll each hot dog in the cornstarch and tap well to remove any excess.
Pour enough batter to almost fill a large drinking glass. Refill the glass as needed. Place each hot dog on chopsticks, and quickly dip in and out of the batter. Immediately and carefully place each hot dog into the oil and cook until coating is golden brown, 4 to 5 minutes. With tongs, remove each corndog to a wire rack set inside a paper towel-lined half-sheet pan, and drain for 3 to 5 minutes.