Heat the vegetable oil in a deep fryer or large saucepan to 350 degrees F (175 degrees C).
Insert wooden skewers into the hot dogs and pat them dry with a paper towel.
In a large bowl, whisk together 3/4 cup of flour, cornmeal, sugar, baking powder, and salt.
In a separate bowl, mix together the egg and milk.
Add the wet ingredients to the dry ingredients and mix until just blended.
Place the remaining 1/4 cup of flour in a shallow dish and roll the hot dogs in the flour, dusting off the excess.
Dip the floured hot dogs into the batter, covering them completely.
Fry the corn dogs in the preheated oil until they are golden brown, about 3 minutes.
Remove and drain on paper towels before serving.