Mix the salmon, eggs, mashed potatoes, onion and garlic in a large bowl. Season with salt and pepper. Stir in the flour to hold the mixture together.
Form the mixture into golf-ball-size balls. Refrigerate 1 hour or overnight.
Heat about 1 inch of peanut oil in a large straight-sided skillet until a deep-fry thermometer registers 325 degrees. Fry the croquettes, in batches, until crisp and golden on one side, 3 to 4 minutes, adjusting the heat as necessary. Turn and cook until golden on the other side, 1 to 2 more minutes. Drain on paper towels.