The Georgia Department of Banking and Finance supervises Georgia state-chartered banks. A bank that is chartered by another state is regulated by that state's banking department.
Banks with a national charter (i.e. normally have "National" or "N.A." in their names) are supervised by the Office of the Comptroller of the Currency (OCC). The OCC has a website HelpWithMyBank.gov, designed specifically to provide answers and assistance to national bank customers. As of July 21, 2011, the OCC is also responsible for the supervision of federal savings banks (FSBs). These institutions normally have "Federal" in their names; however, on rare occasions a state-chartered bank may have the word "Federal" in its name. This would usually be in the case of a conversion to a state-charter where the FSB opted to keep its former name.
Do I Need to Know If My Bank Is Healthy? (Links off-site to the FDIC)