Dear Ms. Nelson,
Thank you for posting your request on History Hub!
Some of the records relating to banks in the custody of the National Archives include the documents of the Records of the Federal Reserve System (Record Group 82) and the Records of the Federal Deposit Insurance Corporation, 1920 - 1993 (Record Group 34). We also searched the National Archives Catalog for “banks” with 3,574 results. For questions about specific record series, please contact the custodial unit listed in the record description. For specific questions about researching banks, you also may post follow up questions here on History Hub.
We hope this information is helpful. Best of luck with your research!