Carter County courthouse is Ardmore. Go to the courthouse and the assessor can show you who owns the surface If you have a deed and legal description that they can reference.
You can check activity on the OK Corporation Commisison Website but OK is not a user-friendly site even though some things have changed there more or less recently. It is nothing as easy as Wyoming or Colorado to use.
They do have an interactive map which you might be able to locate the property with the legal description. If there have been any wells in that area, recent or not so recent, then you should be able to locate it.