If you are being asked about Alabama at the time of secession, the perfunctionary answer to your question is Winston County. However, I believe that answer to be utterly and completely wrong. There was (and still is) debate on the issue of a state's right to leave the union of other states. However, to my knowledge, no one has ever seriously argued the right of county to disassociate itself from a state. Allow me to explain.

There are several obvious and fundamental differences between states and counties. States are sovereign, self-governing political entities which submitted petitions to join the United States. All were either colonies or territories, or in the case of Texas, an independent country prior to becoming members of the Union. All states have executive, legislative and judicial bodies which function in submission to those of the national government.

On the other hand, American history has no record of a group of independent counties which agreed to join together and form a state. State legislatures have constitutional authority to create and dissolve counties, as they see fit. Counties exist at the pleasure of the state. Citizens of each county may establish governing bodies for themselves with authority levy taxes and impose local regulations for residents, but only within certain limits provided by state legislatures. Since no county in the United States was ever a sovereign, self-governing political entity prior to statehood, no county could ever unilaterally assume the authority to leave a state.

However strong Union sentiment might have been among citizens of Winston County and regardless of what might have been said or done at public meetings there, the concept of Winston or any other county leaving a state on any pretext is laughable.