Make the tartar sauce: Mix the mayonnaise, pickles, capers, lemon juice, dill and sugar in a medium bowl. Season with salt and pepper.
Prepare the fish: Rinse the fish with cold water and pat dry lightly. Season with a little salt and pepper.
Whisk the cornmeal, flour and Cajun seasoning in a small bowl. Pour into a medium paper bag.
Add the fish to the bag a few pieces at a time and shake the bag to coat each piece evenly. Transfer the coated fish to a sheet of parchment paper.
Heat 1 1/2 inches of vegetable oil in a deep cast-iron skillet over medium heat until a deep-fry thermometer registers about 375˚ F. Working in batches, add the fish fillets to the hot oil and fry until they start to float and turn golden brown, 3 to 4 minutes.
Remove the fried fillets to a rack set on a baking sheet to drain off any excess oil. Serve with the tartar sauce and lemon wedges.
Whiting is cheap and easy to find in the Low Country, but any good subtle white fish like trout, catfish or flounder will work.