The hot water valve under the sink will not stop the water flow from the faucet.

The valve may be broken, or you may be turning the wrong one. You can turn off the hot water at your hot water heater too.

If it's a stem based valve, the washer is worn or missing entirely. Take the stem to the hardware store. They may replace the washer for free. You pay for parts.

I agree with both of the above. If there is no change at all when you trun the valve then the washer is gone, assuming you have the correct valve in your hand. It may seem too silly but try the cold when you have close the valve, is it still working?