Place the buttermilk, 1/4 tsp. black pepper,salt, and cayenne pepper in a large resealable plastic bag. Add chicken,seal and shake to coat. Chill for 30 minutes or up to 2 hours, if possible.
Place the flour,paprika, mustard,garlic,salt,and remaining pepper in a seperate bag,Add one piece of chicken to the bag,close and shake to coat. Transfer to a wire rack. Repeat with thne remainig chicken pieces.
Preheat oven to 250 F.. heat the vegetable oil in a deep medium skillet to 350 For until a cube of bread dropped into the oil browns in 30 seconds. Add4 chicken pieces to the skillet and reduce heat. Cover and cook for 10 minutes.
Turn the chicken and cook, uncovered until the juices run clear when chicken is pieced with a knife, about 10 minutes longer. Drain the chicken on paper towels. Transfer to a baking sheet and place in the oven to keep warm. Repeat the steps for frying and draining for the remaining chicken pieces. Serve hot.