Special equipment: a tabletop deep-fryer or a deep-frying thermometer
In a large bowl or jumbo resealable plastic bag, combine the buttermilk, 1 tablespoon each of the paprika, garlic powder and onion powder, 1 teaspoon of the cayenne, 1 tablespoon salt and 1/2 teaspoon black pepper. Add the turkey drumsticks and marinate in the refrigerator at least 2 hours and up to overnight.
Preheat a tabletop deep-fryer or fill a large, wide pot with 3 inches of oil; heat the oil to 365 degrees F. Preheat the oven to 200 degrees F. Line a rimmed baking pan with paper towels and place a wire rack on top.
In a large paper grocery bag, combine the flour with the remaining 1 tablespoon paprika, garlic powder and onion powder and 1 teaspoon cayenne, as well as 2 1/2 teaspoons salt and 1/2 teaspoon black pepper. Pat the turkey legs dry and add them to the bag. Fold the top of the bag to seal; shake vigorously to coat the turkey in the seasoned flour.
Remove the turkey legs from the flour and shake off the excess. Fry the turkey in batches, turning occasionally, until deep golden brown, crispy and cooked through (an instant-read thermometer inserted into the center of the meat, avoiding bone, should register at least 165 degrees F), about 16 minutes. Transfer the fried turkey to the prepared baking pan and keep warm in the oven while frying the remaining drumsticks. Return the oil to 365 degrees F between batches.