Pour vegetable oil about 1/4 inch deep into a large skillet and set it over medium heat. Allow the oil to warm until a pinch of breadcrumbs dropped in sizzles but does not smoke, about 2–3 minutes.
In a large mixing bowl, combine the drained canned salmon, eggs, chopped green onions, breadcrumbs, dill, lemon juice, and a generous pinch of salt and pepper.
Mix until just combined—do not overmix, so the patties stay light in texture.
Divide the mixture into four equal portions. With damp hands, gently shape each portion into a compact patty about 1/2- to 3/4-inch thick.
Carefully place the patties in the hot oil, being careful not to overcrowd the pan. Let them cook undisturbed for about 4–5 minutes on the first side, until deeply golden and crisp.
Use a wide spatula to gently flip each patty. Cook for another 3–4 minutes, or until the second side is golden and the patties are heated through.
Transfer the patties to a paper towel-lined plate to drain excess oil for 2-3 minutes.
Serve the salmon patties hot with your favorite dipping sauce or a squeeze of fresh lemon.