Heat 1 tablespoon of oil in a pan over medium-high heat. Cook the haddock for 6 minutes or until just cooked through; discard the skin and bones and flake into small pieces.
Mix the smoked haddock, egg, cheese, chili powder, parsley, scallions, garlic, salt, and black pepper in a large bowl.
Heat the remaining tablespoon of oil and cook fish burgers until they are well cooked in the middle or about 6 minutes. Garnish each serving with a lemon wedge.