How to build on the API of a payment service / exchanger for payment between users on the site?

Question

API

Tell me if there is such a thing - I could not find it in RuNet.
There is a site-forum where people communicate. Everyone has a personal account.
What I need is for one to send money to another through me.
Ideally, it should work like this:
1. One user says to another - send me 10 USD.
2. The second one in the personal account chooses the first one, indicates the amount and sends. Let's say YandexMoney.
3. The first one receives the money, minus the commission for the transfer, to an account convenient for him - for example, to WebMoney.
It would be very good if it was built on the API - then it would give the impression that all the actions are done by the site, and not by a third-party exchanger.