I would ask a few questions, if you don't mind?

What breed is this puppy?

How old?

At what age was he removed from his littermates?

What sort of training class have you attended with the puppy?

Where does this puppy live when you are at home?

When you are not at home?

How is he confined when he is outdoors?

How much exercise does he get in a day?

If you can answer these questions, I might be able to give you some helpful hints.

I would not use a muzzle to curtail barking. IMO a collar would be much more effective and humane.