Prepare Lime Mayonnaise and set aside.
In a large bowl, combine flour, salt, pepper and paprika. Lightly dredge crabs in the mixture and gently shake off excess.
Heat oil in a large skillet to 350° F. Add butter and melt. Add lime juice and mix. Place crabs in a skillet, topsides down. Cook until reddish-brown for about 4 minutes. Gently turn crabs over and cook until done, about 4 more minutes. Drain on paper towels. Serve with lime mayonnaise.
In a small bowl, combine mayonnaise, lime juice, cayenne, salt and lime zest. Set aside for flavors to blend. Serve with cooked crabs.
Contributed by Joyce Taylor