Can I cancel a ticket through the flight booking API if I issued it by mistake?

Yes, in most cases you can, as long as the request goes in quickly and the airline allows it. A ticket issued in error can usually be voided, which means it is treated as though it was never sold and the money comes back without a penalty. That option only stays open for a short window after issue, and once it closes the ticket has to be cancelled and refunded instead, under the fare rules that applied when you booked.

In practice you send the void or cancellation request through the API using the booking reference you got when the ticket was issued. The API passes it to the supplier and returns a status telling you whether the request was accepted, rejected or still being processed. Some suppliers act straight away, others queue it and confirm a little later, so your staff should read the status that comes back rather than assume the ticket has gone.

Whether voiding is possible at all depends on the supplier and the airline behind the fare. Many full service carriers allow it, some low cost carriers do not, and a few suppliers only accept a request that their own team handles first. Anything deducted is set by the airline and the fare, not by your portal, so the same mistake can cost nothing on one ticket and carry a penalty on another.

Ask your supplier which airlines they can void for you and how long that window stays open, and make sure your staff check the fare rules shown at the time of booking before they issue.