Outdoor faucet won't drain even indoor valve is shut off

I'm trying to drain the gardening pipe for the winter.

I disconnected the hose, shut off the indoor water supply valve, and turned on the outdoor faucet to drain water. After two days, there is still water trickling out.

If I shut off the outdoor faucet (no leaking) for a few minutes and then turn it on, there is a little gush of water coming out and then thinning to a trickle again.

Is it a problem with the indoor valve controlling this faucet? For I've tightened it the most I can with a wrentch.

Any information will help. Thanks!

Put a new washer in the inside stop.

Or replace the whole stop.