Combine the dredge ingredients in a shallow dish. Pat the squirrel dry, then dredge each piece in the seasoned flour. Move the coated squirrel to a wire rack. Reserve remaining coating mixture.
Mix the beaten eggs and buttermilk in a bowl or shallow dish. Dip the floured squirrel pieces, one at a time, into the egg wash.
Dip the floured pieces in the buttermilk-and-egg wash before flouring a second time.
After dipping the squirrel in the egg wash, move each piece back into the seasoned flour for a second coat, then return the coated squirrel to the wire rack.
After tossing the squirrel in seasoned flour and dipping it in egg wash, return it to the flour mixture for an extra-thick coating.
Meanwhile, heat 3 inches of vegetable or peanut oil in a heavy pot over medium-high heat. Once the oil reaches 350 degrees, carefully drop the squirrel, a few pieces at a time, into the hot oil. Don’t overcrowd the pan.
Deep-fry a few pieces at a time until the squirrel is crisp and just cooked through.
Fry for 6 to 9 minutes until the coating is golden brown and crispy. Front leg sections will cook faster than hind legs or back sections. We like to serve the fried squirrel with mashed potatoes and green beans. Top the squirrel, potatoes, or both with milk gravy, if desired. If you make the gravy with some of the leftover breading mixture, the paprika will cause the color to be a little bit orange, but the flavor is worth the unusual color.
Serve with green beans and mashed potatoes smothered in gravy made from the seasoned flour blend.