In a deep pan or deep-fryer, heat 2 cups of the oil to 380 degrees F. While the oil is heating, combine the cornmeal, flour, sugar, baking powder, and salt in a bowl. Mix well. In another bowl, beat together the eggs and milk then stir in the oil. Add the flour mixture to the egg mixture along with the onions. Mix well to incorporate all the ingredients. Drop the hush puppy batter by 2-tablespoon sized dollops into the hot oil. Cook them in batches so they do not crowd each other. Cook until golden brown on all sides, turning them as needed. Remove the hush puppies from the oil and let drain on paper toweling. Serve warm.