Mix the salt, brown sugar, paprika, garlic powder, black pepper and cayenne and rub it over all sides of the chicken quarters.
Refrigerate the seasoned chicken uncovered for 4 to 12 hours so the skin dries.
Heat a smoker to 250°F with a mild hardwood such as apple or pecan and brush the chicken lightly with mustard.
Smoke the quarters skin-side up for 75 to 95 minutes until the thickest part reaches 160°F.
Transfer the chicken to a rack and cool uncovered for 20 minutes while heating 2 inches peanut oil in a deep Dutch oven to 375°F.
Lower one quarter at a time into the oil and fry for about 2 minutes, turning once, until the skin is blistered and the meat reaches at least 165°F.
Drain each quarter on a rack, return the oil to 375°F and repeat with the remaining chicken.
Rest for 8 minutes before serving because the skin and bone hold intense heat.