Question: My father and I held a bank account as either-or-survivor. After his death, can the bank ask me for a succession certificate before paying me?
Answer: No. For an either-or-survivor account, the bank should generally not insist on a succession certificate, letter of administration, or probate if death proof and identity are verified.

Supporting evidence:
title: rbi.org.in/CustomerServiceGuidelines.aspx
quote: In such cases, payment to the survivor(s) / nominee of the deceased depositors will be made without insisting on production of succession certificate, letter of administration or probate, etc., or obtaining any bond of indemnity or surety from the survivor(s)/nominee, irrespective of the amount standing to the credit of the deceased account holder the identity of the survivor(s)/nominee(s) and the fact of the death of the account holder, is established through appropriate documentary evidence;
context: ent from the account of the deceased; and
it has been made clear to the survivor(s) / nominee that he would be receiving the payment from the bank as a trustee of the legal heirs of the deceased depositor, i.e., such payment to him shall not affect the right or claim which any person may have against the survivor(s) / nominee to whom the payment is made.
The payment made to the survivor(s) / nominee, subject to the foregoing conditions, would constitute a full discharge of the bank's liability. In such cases, payment to the survivor(s) / nominee of the deceased depositors will be made without insisting on production of succession certificate, letter of administration or probate, etc., or obtaining any bond of indemnity or surety from the survivor(s)/nominee, irrespective of the amount standing to the credit of the deceased account holder.
b. Accounts without the survivor/nominee clause
In case where the deceased depositor had not made any nomination or for the accounts other than those styled as "either or survivor" (such as single or jointly operated accounts), we will adopt a simplified procedure for repayment to legal heir(s) of the depositor keeping in view the imperative need to avoid inconvenience and undue hardship to the common person. Keeping in view our risk management systems, we will fix a minimum threshold limit, for the balance in the account of the deceased depositors, up to which claims in respect of the deceased depositors could be settled without insisting on production of any documentation other than a letter of indemnity.
c. Premature Termination of term deposit accounts

In the case of term deposits, we will incorporate a clause in the account opening form itself to the effect that in the event of the death of the depositor, premature termination of term deposits would be allowed. The conditions subject to which such premature withdrawal would be permitted would also be specified in the account opening form. Such premature withdrawal would not attract any penal charge.
d.Treatment of flows in the name of the deceased depositor
In order to avoid hardship to the survivor(s) / nominee of a deposit account, we will obtain appropriate agreement / authorization from the survivor(s) / nominee with regard to the treatment of pipeline flows in the name of the deceased account holder. In this regard, we will consider adopting either of the following two approaches:
We could be authorized by the survivor(s) / nominee of a deceased account holder