Is there a way to prompt for verification code in Apple Pay instead of calling the bank?

The notification you receive is not from Apple. Apple is not a bank, cannot verify your identity and can’t verify your card. Only the issuing bank can do it. Your bank sends the way they want to be contacted in order to complete the verification.

Adding additional verification

A card issuer can decide whether a credit or debit card requires additional verification. Depending on what’s offered by the card issuer, the user may be able to choose between different options for additional verification, such as a text message, email, customer service call or a method in an approved third-party app to complete the verification. For text messages or email, the user selects from contact information the issuer has on file.

Card provisioning security overview - Apple Support (IN)