For the brine: Combine the buttermilk, hot sauce, garlic, peppercorns and cayenne pepper in a large bowl. Submerge the quails in the brine and refrigerate for 12 hours.
Heat the oil to 300 degrees F in a deep pot.
Combine the flours, salt, black pepper, white pepper and cayenne pepper in a large bowl. Remove the quail from the brine and coat in the flour mixture. Fry the quail, 4 to 5 minutes.