In a medium bowl, combine the catfish, eggs, panko, mayonnaise, celery, onions, parsley, lemon zest, and Worcestershire sauce, stirring with a wooden spoon until everything is evenly distributed.
Season with salt, black pepper, and cayenne pepper to taste.
Divide the mixture into 4 equal portions and form patties about 1 inch thick.
Heat the oil in a large skillet over medium heat.
Cook the patties for 4 minutes, or until the bottoms are browned, before carefully flipping them over. Cook for another 4 minutes so both sides are browned.
Serve on soft buns with lettuce, tomato, and tartar sauce or coleslaw.