How to integrate offline acquiring with a custom cash register solution?

Question

Payment systems

There is a custom cash solution (we take into account the sold goods and print a fiscal receipt for it), written in delphi.
It is necessary to fasten the acceptance of cards to it through a terminal connected to a computer with a cash register program.
All the banks I have bypassed shrug their shoulders, offering their terminals with standard integration with 1C, Rkeeper, etc.
Who has integration experience, tell me in which direction to dig?