There is a thing called cherry eye, where the third eyelid pops out and looks like a big red ugly swelling at the inner corner of the eye. Is that what you are seeing? Does it look big and red and gross and abnormal? If that's what you are talking about, then the dog needs to be taken to the vet, right away. Does it look different in one eye than it does in the other? When you say "some skin," it's kind of hard to picture it.
If it is the third eyelid that you are seeing, it is normal and you do not need to do anything. Is it when the dog goes to sleep that that extra skin kind of rolls up to where you can see it? If so, then yes, that is the third eyelid.
Does the puppy act like he is hurting? Have you taken him to a vet yet for a check-up and shots? Did you just get the puppy this weekend? Because whenever you get a new puppy, he needs to be taken to a vet right away to make sure he is healthy and to get him started on shots and worming.
Good luck, I hope he is fine.
Dogs and cats have an extra eyelid called the 'third eyelid' or the nictitans or nictitating membrane, at the inside corner of their eyes. ...
This is probably what you are seeing. It's quite natural. If there is anything wrong with your dog's eyes, you would probably notice swelling/watering or mucus/redness etc