Prepare the Cod: Steam or poach the cod fillets until they are cooked through and flake easily, about 5–7 minutes. Drain well and let cool slightly before flaking the fish into small pieces with a fork.
Combine Ingredients: In a large bowl, mix together the flaked cod, mashed potatoes, chopped onion, parsley, beaten egg, salt, pepper, paprika (if using), and lemon juice. Stir until the mixture is well combined.
Adjust Texture: If the mixture feels too wet to hold its shape, add breadcrumbs a little at a time until it binds together.
Shape the Fish Cakes: Divide the mixture into equal portions and shape them into patties about ½ inch thick.
Coat the Fish Cakes: Place the breadcrumbs for coating in a shallow dish. Gently press each fish cake into the breadcrumbs, ensuring it’s evenly coated on all sides.
Fry the Fish Cakes: Heat the vegetable oil in a large skillet over medium heat. Fry the fish cakes in batches, cooking for 3–4 minutes per side or until golden brown and crispy. Transfer to a plate lined with paper towels to drain any excess oil.
Serve: Serve the cod fish cakes warm with a squeeze of lemon, tartar sauce, or your favorite dipping sauce. Pair with a fresh green salad or roasted vegetables for a complete meal.