For the rémoulade:
1 cup mayonnaise
3 tablespoons chopped fresh flat-leaf parsley
2 ½ tablespoons grated fresh horseradish
1 ½ tablespoons chopped drained capers
1 ½ tablespoon hot sauce (such as Tabasco)
1 tablespoon Creole mustard
½ teaspoon grated fresh lemon zest plus 1 1/2 tsp. fresh juice (from 1 lemon)
½ teaspoon paprika
1 small garlic clove, grated with a Microplane
For the fried oysters:
Vegetable oil, for frying
1 cup whole buttermilk
2 tablespoons hot sauce (such as Tabasco)
48 fresh shucked oysters (from about two 16-ounce containers), drained and patted dry
1 ½ cups (about 5 5/8 ounces) plain yellow cornmeal
¾ cup (about 3 1/4 ounces) all-purpose flour
1 tablespoon plus 1 teaspoon Creole seasoning
Thinly sliced fresh chives, for garnishing
Stir together mayonnaise, parsley, horseradish, capers, hot sauce, mustard, lemon zest and juice, paprika, and garlic in a small bowl; cover and refrigerate until ready to serve.
Pour oil to a depth of 2 inches in a large Dutch oven; heat oil over medium until a deep-fry thermometer registers 350°F.
Meanwhile, stir together buttermilk and hot sauce in a shallow bowl. Add oysters to mixture; let stand 10 minutes. Whisk together cornmeal, flour, and Creole seasoning in a separate shallow bowl.
Working in small batches, remove oysters from buttermilk mixture, letting excess drip back into bowl. Coat oysters evenly with cornmeal mixture, and place on a large baking sheet. Working in 3 batches (16 oysters per batch), fry oysters in hot oil, stirring occasionally with a slotted spoon, until golden brown, about 3 minutes. Using a slotted spoon, transfer oysters to a baking sheet lined with paper towels. Garnish oysters with chives, and serve immediately with Rémoulade.