Heat the oil to 350°F in a deep fryer or Dutch oven.
In a 1-quart mixing bowl, stir the cornmeal, flour, onion, jalapeño, corn, and eggs until blended. Allow to stand for 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 to a golden brown, about 3 minutes. Remove from the oil with a slotted spoon and drain on paper towels. Keep the cooked hushpuppies warm in the oven while cooking the rest of the batter. Lightly salt to taste before serving.