The above contents are sketchy.
1) It is not known whether you are an award staff or an officer staff. If you are an Officer, the Officer Service Regulation reads - "An officer shall not leave or discontinue the service in the Bank w/o first giving a notice in writing of his intention to leave or discontinue the service or resign. The period of notice required shall be three months and shall be submitted to competent authority as prescribed in these regulations. Provided further that the Competent auhtority may reduce the period of three months, or remit the requirement of notice."
The ingredients are - notice period, submission to competent authority, request for waiver of notice period. Hope you have complied with the above.
2) When the Bank has advised you to stay for further instructions, did you go on sanctioned leave or otherwise.
3) Under whose instructions you chose to remit the amount in lieu of notice period- since this has to be approved by the competent authority.
4) Have you already joined your new employment? Otherwise, you can always report back for duty and persue your letter of resignation.
Unless the above are clearly stated, it is difficult to guide properly.
However, do not lose heart. Termination can be done only after conducting a domestic inquiry and your misconduct is required to be proved .