I want to build an application for consumer card transactions.
For example, my application will offer an opportunity to its users of receiving immediate notifications about the purchases they do with their cards.
Can you suggest to me, which API I have to use to achieve my goal?
For your use case on notifications, I would recommend you to use Visa Transaction Controls (VTC). Please see the links below for more information on VTC.
VTC Overview - https://developer.visa.com/capabilities/vctc
How to Use Visa Transaction Controls - https://developer.visa.com/capabilities/vctc/docs-how-to
VTC API Reference - https://developer.visa.com/capabilities/vctc/reference