Of or relating to or maintained or administered by a county.

ETYM French comté, from Late Lat. comitatus. Related to Count.
Administrative unit of a country or state. In the US a county is a subdivision of a state; the power of counties differs widely between states. In the UK it is nowadays synonymous with “shire”, although historically the two had different origins. Many of the English counties can be traced back to Saxon times. The republic of Ireland has 26 geographical and 27 administrative counties.
A territorial division for local government.