Heat 1/2-inch oil in a large, high-sided skillet to 365 degrees F.
Mix the mayonnaise, pickle relish, lemon juice, mustard, hot sauce and scallions in a bowl. Season with salt and pepper. Refrigerate the tartar sauce until ready to serve.
Sprinkle the catfish fillets on both sides with salt and pepper.
Mix the flour with paprika and some salt and pepper in a shallow dish. Whisk together the eggs and milk in a second dish. Place the cornmeal in a third dish. Dredge each fillet in the seasoned flour first, then the eggs and finally the cornmeal.
Gently place the fillets, spaced apart, in the hot oil. You will probably have to cook the fillets in two separate batches. When the undersides are crisp and golden brown, 2 to 3 minutes, carefully flip the fillets and continue frying until cooked through, another 2 minutes.
Blot the fried catfish on a paper-towel-lined plate. Sprinkle with salt. Serve with the tartar sauce on the side.