Remove any large bones or skin from the drained salmon, then place it in a large mixing bowl. Flake the salmon with a fork to break up larger pieces.
Add the diced green onion, celery, beaten eggs, tarragon, seasoning salt, pepper, and gluten-free breadcrumbs to the bowl with the salmon. Gently mix with a fork or your hands until all ingredients are evenly incorporated and the mixture holds together.
Portion out the mixture and shape into 10 equal-sized patties, each about 3 tablespoons or roughly 2 1/2 inches across. Handling the mixture with slightly damp hands can help prevent sticking.
Add the oil to a large nonstick or cast-iron skillet and heat over medium heat until the surface of the oil is shimmering and hot but not smoking.
Carefully arrange the patties in the hot oil, being careful not to crowd the pan. Fry for about 2-3 minutes per side, or until the patties are golden brown and crisp. Work in batches if necessary, adding more oil as needed for each batch.
Transfer the cooked patties to a plate lined with paper towels to drain excess oil. Let cool for about 5 minutes before serving.