Drain the juice from the can of salmon into a mixing bowl.
Crumble the crackers and add them to the juice. Stir until the crackers have absorbed the juice.
Add the egg.
In a separate bowl, break apart the salmon and remove and skin and bones. Add the salmon to the cracker mixture.
Season with salt and pepper to your preference.
Form the salmon mixture into patties that are roughly 2-inches wide and 1/2-inch thick.
Fill a large skillet halfway with oil. Heat the oil over medium high heat until it reaches 375 degrees on a thermometer.
Working in batches, add the salmon croquettes to the hot oil. Fry for 1-2 minutes, flip the patties, and fry for an additional 1-2 minutes until the patties are golden brown. The internal temperature of the patties should be 145 degrees F.
Drain the fried salmon croquettes on a layer of paper towels while you fry the rest. Season the tops of the patties with additional salt and pepper if desired.