In a bowl, gently combine salmon, egg, breadcrumbs, mayonnaise, Dijon mustard, parsley, green onion, garlic powder, paprika, salt, pepper, and lemon juice.
Shape the mixture into 8 even patties and chill in the refrigerator for 15 minutes to help them hold their shape.
Heat olive oil in a skillet over medium heat and cook the patties for 3 to 4 minutes on each side until golden brown and crispy.
Optionally, bake the patties in a preheated oven at 400°F (200°C) for 12 to 15 minutes, flipping halfway through cooking.
For the optional sauce, mix Greek yogurt or mayonnaise with lemon juice, garlic powder, and chopped dill.
Serve the salmon fish cakes hot with the creamy sauce, salad, rice, or in a sandwich as desired.