To brine the chicken: In a large bowl, whisk the water, hot sauce, salt, and sugar until the sugar dissolves. Submerge the chicken in the liquid and refrigerate for at least 1 hour and up to 6 hours.
To prepare the fried chicken: Heat the oil in a small saucepan over medium heat until shimmering. Add the cayenne, paprika, garlic powder, sugar, and 1 teaspoon salt. Cook, stirring, until fragrant, about 30 seconds. Transfer to a small bowl and reserve.
In a large resealable plastic bag or paper bag, combine the flour with 1/2 teaspoon salt and 1 teaspoon freshly ground black pepper. Add the chicken in batches and shake well until all the pieces are evenly coated.
Add enough oil to a cast-iron or other heavy skillet to come 1/2 inch up the sides. Heat the oil over medium heat until it reaches 365°F. The oil’s ready when a little flour dropped in bubbles and sizzles steadily.
Remove the chicken from the flour, shaking off excess. Carefully place the chicken in the oil, skin side down. Repeat, adding just a few more pieces to the pan. You don’t want to crowd the pan. Keep adjusting the heat to keep a steady sizzle and to maintain 365°F. Cook until browned on the bottom, about 3 minutes, then carefully turn each piece over. Cook until browned on the bottom, about 3 minutes, then continue cooking and turning to evenly brown until cooked through, about 10 minutes total.
Crumple up some paper towels and drain the chicken on them. Repeat with the remaining chicken, replenishing and reheating the oil between batches. Transfer to a serving dish and drizzle with the reserved spice oil. Serve hot.