Cut fish into 3-inch strips. Sprinkle evenly with 1 teaspoon Greek seasoning, 1 teaspoon salt, and ½ teaspoon pepper.
Combine flour, cornmeal, baking powder, remaining 1 teaspoon Greek seasoning, ½ teaspoon salt, and ½ teaspoon pepper in a large bowl; stir well. Add cold beer and beaten egg, stirring until thoroughly blended and smooth.
Pour oil to a depth of 2 to 3 inches into a Dutch oven; heat to 375°F.
Dip fish strips into batter, coating both sides well; shake off excess. Fry fish in batches for 2 minutes on each side or until golden brown (do not crowd pan). Drain on paper towels.
Spread top half of each bun evenly with tartar sauce. Place 1 lettuce leaf and 1 tomato slice on bottom half of each bun; top each with 2 fried fish strips and top halves of buns.