Pour oil to a depth of 1 1/2 inches in a stockpot or Dutch oven. Place it over medium-high heat, and heat to 375°. Preheat oven to 200°. Place wire racks on baking sheets, and set them aside.
While the oil is heating, prepare the coating for the fish. In a wide bowl, mix corn flour, 1 teaspoon salt, black pepper, and red pepper.
Prepare the hush puppy batter. Mix the egg and buttermilk well in a medium-size bowl. Stir in cornmeal until well blended. Stir in onion. Place remaining 1 teaspoon salt, baking powder, and baking soda in a small bowl, and set both bowls aside while you fry the fish.
When the oil reaches 375°, dip each fish or fillet in the seasoned corn flour, coating it all over but shaking off any excess. Carefully lower each piece into the hot oil. Fill the pot but do not crowd it; the oil should bubble up around each piece of fish. Monitor the temperature closely so that it stays between 365° and 375°. Fry the fish until it is golden all over, about 2 to 3 minutes on each side, depending on the size of the pieces. Set aside any of the remaining corn flour.
Remove the fish from the oil in the same order that the pieces were immersed, using a wire-mesh strainer, tongs, or any tool that will allow you to hold the fish over the pot so excess oil can drain. Immediately place the pieces on a wire rack, and place in the oven to keep warm.
Continue frying until all of the fish are done, always waiting for the oil to return to the proper temperature before adding more. Then proceed with frying the hush puppies.
Add the reserved baking powder mixture to the hush puppy batter and mix well. Then add the leftover seasoned corn flour to the batter, a little at a time, until the batter is thick enough to be spooned. This will take about 1/4 to 1/2 cup of the remaining corn flour.
Make sure that the oil has returned to 375°, and then drop the batter by spoonfuls into the hot oil, using 2 teaspoons: one to scoop up the batter and the other to scrape it off and into the oil. Fry the hush puppies until they are golden brown all over, about 3 minutes, again carefully monitoring the oil, and then place on a wire rack.
You probably won't have to put the hush puppies in the oven to stay warm because your guests will be picking at them. Besides, they stay warm a fairly long time, and there are plenty to go to around. Repeat the process until all the batter is fried. Garnish with lemon wedges and parsley sprigs, if desired. Serve the fish and hush puppies immediately.
Note: Corn flour is the finest grind of cornmeal; in Louisiana it's called "fish fry." If you can't find it, you can make your own by grinding cornmeal in a blender or food processor.