Heat the oil to 350 degrees F. in a deep-fryer or Dutch oven.
In a 1-quart mixing bowl, stir the cornmeal, flour, onion, jalapeno, corn, and eggs, until blended. Allow to stand 5 minutes.
Drop the batter by teaspoonfuls into the hot oil. Don't overcrowd; leave room for the hushpuppies to be turned. Cook the hushpuppies until golden brown, about 3 minutes. Remove from the oil with a slotted spoon and drain on paper towels. Keep the cooked hushpuppies warm in an oven while cooking the remaining batter. Lightly sprinkle with salt and pepper, to taste, and transfer them to a serving dish. Serve with Paula Deen's Sweet and Spicy Chili Sauce, if desired.