In a small bowl, stir together the mayonnaise, ketchup and relish, adding hot sauce to taste. Set aside.
Cook the sausage patties according to the package instructions. Meanwhile, split the dinner rolls and cut each slice of cheese into 4 equal squares. Spread some of the sauce on the split sides of the rolls. Lay a slice of cheese on the bottom of each roll.
When the sausage patties are ready, lay one in each roll, arrange a few pickles over the sausage and top with the other roll half. Serve immediately.