Wash the chicken parts thoroughly and dry them on paper towels. Heat the fat to 380 degrees in a heavy cast-iron skillet. Place the flour, cornmeal, and seasonings in a brown paper bag. Add the chicken pieces, a few at a time, and shake well to ensure that each piece is coated with the seasoned flour.
Put the chicken pieces in the frying pan and fry uncovered for 20 to 25 minutes, turning occasionally to make sure that each side is golden brown. Remove the chicken pieces and drain them on pieces of brown paper bag. Serve hot.