Please don't be put off by some of the prior responses.
Ardmore was a town on the old Central Railroad (not to be confused with the Central of Georgia). The Central Railroad was a predecessor of the Savannah & Atlanta RY, which was acquired by the Southern Railway, which merged with the Norfolk & Western to become the present-day Norfolk Southern System. And, yes, there is a railroad there today, and "Ardmore" is the junction of the shortline up to Sylvania, and the NS's main line between Savannah and Macon / Atlanta, and Augusta, GA / Columbia, SC.
During the Civil War, both of Sherman's two wings of his Army (aka "The Marauding Horde") passed through Effingham County on the infamous march across Georgia to Savannah.
Sherman's army used the Central Railroad to transport equipment and supplies that had been plundered from the areas that his army had passed through, and totally destroyed the sections of railroad behind them so that it would be of absolutely no future use to the "enemy".
Yes, Sherman's army did burn and destroy anything and everything that was considered to be of militiary or economic sigificance, usage or value. And, yes, sometimes the fires got out of control and accidentially burned a lot more than was intended to be destroyed, but hey, that's what total warfare is all about! So, it is very possible that the entire town was burned and destroyed, whether accidentally or on purpose!
My suggestion is that you contact the Georgia Historical Commission, as the Commission has extensive files on the details of Sherman's little "picnic" between Atlanta and Savannah. If the town of Ardmore was destroyed by Sherman's "troops", they would have a record of the happening.
Regarding coins, I'm not aware of any cities in Georgia during that period of time that minted coins, simply because of a historical thing against taxation, the cities had no way to create the monetary wealth necessary to give value to the coins.
On the other hand, local banks affiliated with the Georgia Banking Company did have the financial wealth and reserves to mint and distribute coins for general usage in the local area. It was a way for them to keep payroll monies and other money being exchanged in the local area, rather than being spent somewhere else.
And, large companies that operated company stores (commissaries) also minted their own coins, and paid most (and in some cases, all) of their workers' salaries in their own coins, which forced the employees to buy their food, clothing, and other needed supplies from the company store (at inflated prices), rather than in the general community. Sawmills, cotton ginning mills, turpentine companies, and similar operations often had company stores, and their own coins for use in the company stores.
So, it is my guess that if coins were minted in the Ardmore area, it was by a local bank or large employer with a company store; and not by the city.
Again, if you haven't already, please check with the Georgia Historical Commission. They are a real treasure trove for the type of information that you are searching for.
Good luck and best wishes!