There are hospitals nearby in Alexandria Bay, Carthage and Watertown.
New York State Hospital Profile
Samaritan Hospital in Watertown is probably the best bet. There are hospitals in Syracuse, which is about an hour and a half away from Clayton, that may provide the healthcare that your son needs.
New York State Hospital Profile
Here is a guide that shows hospitals by county in NY State:
New York State Hospital Profile
Here is information from Bassett Hospital in Cooperstown that may be of interest to you, if you are open to other parts of Upstate NY:
Bassett Healthcare Network | Neurosurgery | Cooperstown, NY