Bank fraud is a growing problem and something we all need to be aware of, both for ourselves and loved ones.
So much so that the ABA has a (somewhat corny) website and ad campaign called "Banks Never Ask That"
https://www.banksneveraskthat.com
I'll add this:
Bank locally, at a bank or credit union that's headquartered in your State (or Province) and small enough that you can know them.
Keep the phone number of your local branch. Maybe even grab a business card from your local branch manager, so you have a name.
Beyond branches, local banks have local 'Operation Centers' that manage and process the back end of your banking transactions - They're staffed with friendly people who can help you. Have those 'call center' numbers handy, too.
Use online banking safely and monitor your accounts regularly.
Be careful out there!
Re Banking security:
Excellent advice!