my kitchen sink is leaking even with the shut off valve turned off?

My water is running in the kitchen faucet. Tried turning the shut off valve off to replace washer, but there is still water running out of the faucet(a small amount). There are separate shut off valves for hot and cold. I am assuming that the valve is the culprit since we have tried replacing the entire fitting inside of the faucet. Is this the problem or could there be something else I am missing?

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