I replaced faucet and turned on main h20 valve then turned handle for cold water on and it went on but when handle is turned in off position it still comes out

One handle or two knobs? What's the name and model number? Back to you, Tom

speedball1 the faucet is delta although I don't have a specific model it is similar to Orleans Centerset Bath Faucet : Bath Products : Delta Faucet cenerset it has separate handes for the hot and cold water

I would return it back to the store for replacement it is under warrant, other wise close the angle valve remove the stem turn on the water for a few seconds to flush out all the debris close the valve check inside for an debris remove if any, assemble the faucet and check if it works, good luck.

John