Whisk together buttermilk, mustard, salt, pepper, and cayenne in a bowl.

Pour buttermilk marinade into a resealable plastic bag. Add chicken pieces, coat with marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator for 2 to 8 hours.

Combine flour, baking powder, garlic powder, and onion powder in another resealable plastic bag; shake to mix thoroughly.

Working with one piece at a time, transfer marinated chicken to the dry ingredient bag, seal the bag, and shake to coat. After all chicken pieces are coated, repeat the process by dipping them in buttermilk marinade and shaking in the dry coating again.

Heat oil in a large frying pan over medium-high heat. Fry chicken in batches in hot oil, turning chicken occasionally, until golden brown and juices run clear. An instant-read thermometer inserted into the meat should read at least 165 degrees F (74 degrees C).