In a medium bowl, combine the tuna, egg, cheese, and salt. Mix thoroughly with a fork until well blended.
Divide the mixture into 4 equal portions and shape each portion into a patty about ½ inch thick.
Heat a large skillet over medium-high heat for about 3 minutes, until hot but not smoking. Add the butter and swirl to coat the pan.
Place the patties in the skillet and pan-fry for 2 to 3 minutes on one side, or until golden brown. Flip and cook for another 2 to 3 minutes until browned on the other side.
Serve immediately, either as a handheld snack or with a fork and knife for a light meal.