I have a two knob faucet and the cold side won't turn off completely. I have a small looks like Allen screw in side of faucet but I can't get it to turn. How can I stop it?

Two handles tells me that its likely a faucet with washers. Once a washer cracks or gets brittle is can leak, bad brass seat is also high on the list. Do you know how to reseat a valve or replace the washer? HowStuffWorks "How To Repair a Faucet Valve Seat"