Does his paws smell like fritos corn chips @ all? Was a skin scraping done?
If yes to corn chips smell, it could be yeast....it's very itchy & smelly. Yeast thrives in moist places, so the constant licking, dampness can exacerbate it. Also, high carb starchy diet are fuel for yeast. So all grains, potatoes (including sweet potatoes) must be eliminated. There are also higher than normal carb veggies & fruits, like carrots that needs to be eliminated.
Linking a great article/ video just in case:
Chronically Itchy or Smelly Dog? It Could Be Yeast Infections
If it doesn't smell like corn chips, then it could be his nails. Might need trimming. If it gets too long, it bothers them when they walk.
If his nails are trimmed, then it could be just boredom or OCD, just like human baby thumb sucking. My vet said so! LOL