Sift all the dry ingredients together: cornmeal, flour, salt, sugar, baking powder, baking soda, and the peppers into a mixing bowl. Stir in the beaten eggs combined with the buttermilk, the fat, and onion.
Preheat oil to 365°F (185°C). If you are using a deep skillet, allow about 2 inches (5 cm) of fat for frying. Drop the batter by teaspoonfuls into the hot fat. The hushpuppies will sink to the bottom, rise to the top, and turn of their own accord as they cook. When golden brown, after a total cooking time of about 3 to 5 minutes, remove with a slotted spoon and drain on absorbent paper. Do not over-brown, as the hushpuppies will turn bitter. They can be held on brown paper in a warm oven for a few minutes, but serve as soon as possible.