In a large bowl, whisk cornmeal, flour, and salt, and remove any lumps. In a separate bowl, add onion, jalapeño, corn, cheese, buttermilk, and egg. Mix well. Pour the wet ingredients into the dry ingredients and stir well. Allow the batter to stand at room temperature for 8 to 10 minutes.
Meanwhile, in a deep skillet or deep fryer, heat oil to 375 degrees Fahrenheit. Make sure there is enough oil for the hushpuppies to float. Set a wire cooling rack over a baking sheet lined with paper towels. Drop the batter by tablespoon into the hot oil until golden brown. Remove the hushpuppies to the cooling rack and continue frying.