Is There A Data Set That Lists The Zip Codes Of All The Appalachian Counties In The US?

I have a data set of hospitalized patients with their zip codes, we’re trying to determine which of them live in Appalachian counties. I have been unable to find a doc that includes all the zip codes of the Appalachian counties, but I did find this list of the county names however.

Anyone have any insight on where to find that info? Thank you!