Place the fish fillets in the freezer until firm, about 30 minutes, then finely chop. (If you bought them frozen, thaw for half an hour at room temp before cutting.)
Place the fish in a bowl along with 1/4 cup of the panko, 1 of the eggs, and the mayonnaise, mustard, salt, onion powder, and cayenne pepper. Use your hands or a large spoon to combine.
Shape the fish mixture into 1 1/2-ounce finger-shaped sticks. Set on a sheet pan and refrigerate for 30 minutes to firm up.
Meanwhile, beat the remaining 2 eggs in a shallow pie pan. Place the remaining cup of panko in a second pie pan and the flour in a third.
When the fish sticks are firm, roll each stick in the flour, then egg, followed by the panko and place back on the sheet pan. (If you're not ready to cook, cover with plastic wrap and refrigerate for up to 6 hours.)
Place the oil in in the Dutch oven, attach a thermometer and bring to 350°F over medium-high heat. Line a half sheet pan with paper towels, then place a wire cooling rack upside-down on the paper towels.
Fry half of the fish sticks until golden brown and they register 145°F on an instant-read thermometer, about 2 minutes. Using a spider, transfer to the prepared rack. Repeat with the remaining fish sticks. Serve hot with your favorite tartar sauce.