Using API -> Pay for order

I found the Using API documentation ( with basic steps to work with. The last step is to complete the order. But I can’t find how to pay for the order throw API. Also I found this controller: sylius.controller.payum::prepareCaptureAction. But I can’t find any api calls for it. Do these API calls exist or I should create it by myself?
Any example would be great.

Thank you!