Scam. Pretend to be a call from bank wanting to verify a transaction. Female, Indian accent. I feel suspicious and lied saying I don't have an account with them. Then the girl claimed she's from another bank. Straight away you know something is wrong but I play along.

She doesn't have a way to verify her identity or mine but asked me for information to verify my ID. She said she has sent me a email which is not true.
DO NOT give any information about yourself even if she said it is to verify your ID. They need to prove theirs first.
They seem to collect information about you through different calls to build up your profile for scamming you in future with other call IDs.
If it is the bank, they must have some other ways for you to be able to identify them. e.g. Asking you to call to a number that you can find from the bank's official website.