In a large mixing bowl, combine the flaked salmon, breadcrumbs, beaten eggs, mayonnaise, Dijon mustard, chopped green onions, parsley, lemon zest, salt, and pepper. Mix until well combined.
Shape the mixture into patties, ensuring they hold together well. If the mixture is too wet, you can add more breadcrumbs.
Heat vegetable oil in a skillet over medium heat.
Carefully place the salmon patties in the skillet and cook for 3-4 minutes on each side, or until they are golden brown and cooked through.
Once cooked, transfer the patties to a plate lined with paper towels to absorb any excess oil.
Serve the Fried Salmon Patties hot, garnished with fresh parsley and lemon wedges on the side.