Subscriptions are auto-renewed, so you will need to cancel any subscription on the website and you can also check for their refund policy. Apple Pay simply securely transmits the transaction between the merchant and the bank that you have designated to be used for Apple Pay. When you use Apple Pay, you will need to double click the side button followed by verification using FaceID/TouchID or Passcode, so it is not something that is done by accident. You may have inadvertently signed up for a subscription and that transaction will continue between the merchant and your bank without any intervention from Apple Pay. You can also contact the bank that was used for the card that was charged.
As for a refund, that will either need to come from the merchant or the bank of the card used if they let you dispute the charge. In some cases you can dispute fraudulent charges with a bank card, but they will be able to see that it was verified using either FaceID/TouchID or your Passcode, and that is all that is needed for authorization. Your bank will honor a subscription and continue to bill you for that subscription even if you did not mean to sign up for it. Contact them for further assistance with that matter if you are unable to cancel the subscription on your own.