I have a 1993 98 full size the car rides good when the gas tank is full , but when my gas meter is on 1/4 tank and I stop to hard or I turn the corner it does not mater left or right the car cuts off. So my question is what is making that happin and what can I do to stop it?

I would make sure and change the fuel filter. A clogged fuel filter can affect both flow and pressure. If either of these drops very much, due to a clogged fuel filter, the fuel rail is not properly pressurized with the proper amount of fuel and the car dies. Fuel filters are grossly overlooked by many people, but they can stop a vehicle in its tracks if not regularly changed. After making sure the fuel filter is okay, I would check the car's fuel pressure. It could be the fuel pump is weak. Frequently, fuel pumps weaken and eventually burn out, because the fuel filter is not changed regularly. I would also make sure and install fresh ACDelco plugs in the car. Replace platinum plugs at about half the manufacturer's recommended mileage.