Hi and welcome to YT
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In adult dogs, paw chewing/licking is due to allergies as the histamine response causes symptoms in their paws and they then need relief via chewing/licking.
In puppies though, allergies are almost impossible due to the immaturity of their immune system. How old is this puppy?
No matter the age though, this pup needs to see a vet ASAP as this could also be mites/mange...which will spread and be quite devastating.