I think we should list out basic security measures and tips we each follow - maybe create a knowledge-bank of sorts for dealing with this menace.
1. No bank will EVER ask you for your username or password/pin/otp. this is true for any medium (phone, email, sms etc.)
2. check links are secure i.e. the web page starts with "https" and not "http"
3. the OTP generated for online transactions is for your eyes only and any request for it is to be immediately treated as an attempt at defrauding you. keep it safer than nuclear launch codes. the branch manager or even the president/ceo/owner of the bank cannot and will not ask you for your password/pin/otp. it is unique and private - even the prime minister cannot demand your pin/otp number.
4. if you are getting calls from people who have your name/last 4 digits etc. then report it to your bank and request a new card asap. this is especially true for calls asking for otp - as that means they have your card no, exp date AND the cvv #. otp is all that's left for completing the transaction.
5. as always, change passwords/pins regularly - in fact just change your cards every now and then.
6. writing down pins/password is generally a bad idea but sometimes it is necessary so in that case make sure it's written on something that will never leave the house or be in anyone else's hands/eyesight. phone, laptop, notepad etc are to be avoided.
7. paranoia and google are a deadly combo - treat all financial related contact as suspicious and do a quick google of anything you are encountering for the first time (web-pages, links, apps etc.) and like the op always ask around especially the bank itself.
8. these callers use a 'can you prove your identity' approach to confuse you about their own legitimacy. You might be tempted to ask them to prove that they are genuine but don't bother. 100% (not 99.99%) of these calls are fraudsters. you'll only be wasting your time. just say "i'll be right back" and leave them hanging on the line (at least they wont be trying to scam an elderly pensioner for a few minutes).