I'll try to share some of what I know about this process. I do not know if it will be suitable for the country you want to implement.
In Brazil, we work in the following scenario, homologated and defined according to location-specific rules and central bank authority.
The Microsoft Brazilian localization offers an "plug-in" with a brazilian partner that interfaces with several credit card operators (Visa, Mastercard, American Express, Telecommunications companies for mobile phone credit...).
Payment POS is made by this credit card service. The service only sends to POS if the payment with the card was approved or not, to finalize the purchase. This service does all the management with the credit card operators and offers reports for auditing and conferencing.
In the next day, following the operation, the payment of credit card transactions is deposited to the company's bank account by the card operators (totalized by the number of transactions, or transaction by transaction, depends on the card and the type of transaction.). A bank file statement is import and performed to reconciliation values with AX.
Also check this links with related subjects:
http://gyaneshmsd.blogspot.com.br/2016/10/payment-methods-configuration-in.html
https://technet.microsoft.com/en-us/library/jj680904.aspx
https://community.dynamics.com/ax/f/33/t/241318
https://technet.microsoft.com/en-us/library/jj729753.aspx
I Hope this Helps!
Regards,
Rodolfo Recalde.