Whisk buttermilk, hot sauce, and 1 teaspoon salt in a large bowl. Add chicken; refrigerate 4 to 12 hours.
Remove chicken 30 minutes before frying. Whisk flour, paprika, garlic powder, black pepper, cayenne, and remaining salt in a shallow pan.
Lift pieces from buttermilk; let excess drip 5 seconds. Press firmly into flour until no wet patches remain.
Rest coated chicken on a rack 15 minutes to hydrate flour and help it cling.
Heat 3/4 inch oil in a 12-inch cast-iron skillet to 325°F. Add half the chicken skin-side down without crowding.
Fry 7 to 9 minutes per side, maintaining oil at 315°F to 330°F, until deep golden and at least 165°F beside bone.
Drain on a clean rack; return oil to 325°F. Repeat with remaining chicken.
Rest fried chicken 8 minutes to settle juices and firm crust.