Depending on what you mean, but as a very quick answer without any specifics: on average less than 1 kilobyte.
If you hold a magnetic card, the magnetic reader will read either track 1 or track 2 from the card. Track 1 - 79 characters, where track 2 - 40 characters. For a magnetic card, this is obviously all the data read from the card. See Magnetic stripe map .
For a chip card, many messages (APDUs) are exchanged between the payment terminal and the card chip. I don’t remember how much data was accurate, but it is in the order of hundreds of bytes, not kilobytes. They are indicated in the specifications of EMV, again Wikipedia gives the correct idea: EMV .
If you are talking about the connection between the payment terminal (or POS) and the server for authorization online , this is again different. The communication amounts are approximately comparable with the communication of chips, again in the order of hundreds of bytes, and not in kilobytes. They use the ISO 8583 format, but there are many differences between countries, so the standard is not accurate.
And again, if you are talking about a cleaning batch material that is sent at the end of each day, this is also an ISO 8583 message, but it is in ASCII format. Each line has one transaction, and one transaction is usually less than 200 characters.
And if you are talking about the connection between the POS and the server or all the saved data or something like that, then it completely depends on the PIC!