Rinse the frog's legs and pat dry; set aside. In a large resealable bag, combine the saltine cracker crumbs, flour, cornmeal, onion, salt and pepper. Shake to mix. In a shallow bowl, whisk together eggs and milk.
Heat the vegetable oil and peanut oil in a large skillet over medium-high heat. The oil should be about 1/2 inch deep.
Dip the frog's legs into the milk and egg, then dip into the cracker mixture until evenly coated. Carefully place them in the hot oil. Cook until golden brown on each side, about 5 minutes per side. If the legs start to brown too quickly, reduce the heat to medium. Drain on paper towels before serving.
