Rinse the catfish fillets and pat them dry.
Mix the 3/4 cup cornmeal and 3 teaspoons Cajun seasoning in a large bowl or bag. Add the fillets, two at a time, and shake to cover them in the mixture. Repeat until all of the fillets are coated.
Place the fillets in the air fryer basket. Cook at 390°F for 15 minutes, flipping halfway through, until the fish reaches 145°F. Set aside, then cut into bite-size pieces.
Slice the tomatoes about 1/3 inch thick, then cut each slice into four pieces.
Set up three bowls: flour in the first; the beaten egg and water in the second; the 1/4 cup cornmeal, panko and 1 tablespoon Cajun seasoning in the third.
Working in batches of two, dredge the tomatoes in the flour and shake off the excess. Drop them into the egg mixture and stir to coat, then toss in the cornmeal mixture. Place the breaded tomatoes on a plate. Repeat.
Spray the air fryer basket with olive oil and gently place the breaded tomatoes in the basket. Cook for 6 minutes at 390°F.
Layer fried green tomato, pimiento cheese, arugula and catfish on skewers, and repeat until all of the ingredients are used.