Rinse and dry chicken pieces with paper towels. Combine the buttermilk with 1 teaspoon salt. , 1/4 teaspoon black pepper and paprika and 1/8 teaspoon cayenne pepper in a large bowl. Add chicken, turn to coat evenly. Cover the bowl, refrigerate a minimum 2 hours or overnight, turning the pieces occasionally.
Put the flour in a pie plate along with the remaining salt, pepper, paprika and cayenne. Stir well.
Place three layers of paper towels on a baking sheet. Pour the oil into a 10-12 inch cast-iron skillet or Dutch oven. You should have 1 to 1 1/12 inches of oil. Heat the oil over medium high heat until it registers 365 degrees.
Remove the smaller pieces of chicken first, letting the excess marinade drain off over the bowl for a moment. Dredge in the flour mixture, turning to coat evenly. Shake off excess flour. Put the pieces skin side down in the center of the hot oil. Proceed with remaining chicken pieces. Do not crowd the skillet.
Don't move the chicken until the coating is set and looks firm, 4-6 minutes. Check the underside by lifting with tongs. Turn the pieces when they are a deep golden brown. When both sides are a deep golden brown, 17-25 minutes depending on size of each piece, remove and place on cookie sheet with paper towels to drain.