In a medium bowl, mix the cornmeal, flour, baking powder, pepper, salt, sugar, baking soda and cayenne. In another bowl, gently mix the buttermilk, scallions and eggs.
Whisk the wet and dry ingredients together until just combined, then rest the batter for 10 minutes.
In a 6-quart stockpot, pour enough oil to fill the pan about a third of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 350 to 360 degrees F. Drop small scoops or rounded tablespoons of the batter into the oil in batches of eight. As soon as the hush puppies start to float, use tongs to rotate and cook until both sides are crisp and light golden brown, 60 to 90 seconds. It helps to put a pasta strainer on top of the hush puppies at this point to keep them submerged. Use a slotted spoon to remove the hush puppies, and transfer to a clean brown paper bag to remove excess grease. Repeat for the remaining batter, about 24 hush puppies total.
Serve the hush puppies steaming hot.