Yes, Public Sector Banks are covered under RTI Act 2005. However, you cannot file RTI to Private Banks.
You can file RTI to a Public Sector Bank other than to obtain information pertaining to a Third Party or Exemption under Section 8 (1) (d).
To know more about the procedure to file RTI Application, please visit https://onlinerti.com
To know more about the procedure to file RTI to Nationalised Banks under Central Government, please refer https://onlinerti.com/how-to-file-rti-online-for-center