My Shih Tzu is almost 2 years old and had her 1st litter 4 days ago. She keeps moving one pup, yet still nurses him. No physical problem or cleft mouth. I’m scared she’ll eat him, I’ve heard horrible stories about that.
Going along with what Elmy said in the comments:
Mothers can detect birth defects as they can detect cancer in humans, You should get it checked out. It could be that the mother is protecting the one pup from the other pups for some reason although I have no idea why. If I could guess, it's because the pup doesn't need to drink that much so the mother would let the pup have the rest of the milk. I would still get the puppy checked out by a veternarian just in case.