Using a fine-meshed sieve over a large bowl, sift together the cornmeal, flour, sugar, baking powder, baking soda, salt, and cayenne. Using a rubber spatula, stir in the buttermilk, egg, and scallions, until a batter is formed. (Take care not to over-mix the batter or the hushpuppies will be dense.)
Pour the oil for frying into a large heavy-bottomed pot to a depth of 2 inches. Place over medium heat and heat to 375 degrees F. Working in small batches, using a greased teaspoon, drop spoonfuls of batter into the oil, turning once, frying until golden brown and cooked through, about 4 minutes per batch. Using a slotted spoon, transfer the hushpuppies to a paper towel-lined plate and sprinkle with salt. Serve immediately.
Cook's Note: Using a greased spoon (vegetable oil spray works well) helps to release the batter from the spoon. Additionally, if you drop the batter off of the tip of the spoon it will form ball shapes; if dropped off the side it will form oblong shapes.