For the corndogs: Pour the oil into a Dutch oven fitted with a deep-fry thermometer. Place over medium-high heat and preheat to 375 degrees F.
Insert a toothpick lengthwise into the center of each cocktail frank, leaving about 1/2 inch of toothpick exposed.
Mix together the corn muffin mix, buttermilk and egg in a medium bowl to make a batter. Pour the batter into a small cup to make it easier to dip the franks.
In batches, hold onto the toothpick and dip a frank into the batter. Slowly turn until the frank is evenly coated. Drop into the hot oil and fry until golden brown, 1 to 2 minutes per side. Drain and place onto a cooling rack over a baking sheet. Repeat with the remaining franks and batter. Let cool slightly.
For the sweet and spicy mustard: Whisk together the hot pepper jelly and mustard in a small bowl.
For the fry sauce: Whisk together the ketchup, mustard and Worcestershire sauce in a small bowl.