How can I cancel Apple Pay payment towards an unintended subscription?

Apple Pay is simply providing a merchant the token your bank provided you when adding the card. That way the merchant does not have your actual account number to your card that may be compromised through a breach or nefarious actor who could sell that information. Your card account number is also not viewable on your device. That is the benefit of using Apple Pay to secure your transaction details, but you do not dispute a charge through Apple Pay. That is done the same way as any other credit card transaction where you first contact the merchant, and if failing to find a resolution, then you dispute the charge with the card that is being charged. Any refund the merchant provides does not go to Apple Pay, it goes directly to your card.

You need to go back to the website you subscribed on and cancel it there, likely by logging into your account there.

You used Apple Pay to allow a subscription on a 3rd party site, so yes, you in fact did sign up for it, event it was unwittingly. Whatever subscriptions you activate in that way are your own responsibility to understand and manage.

And after contact with them, if there is then a dispute between you and service that offered the subscription, that then becomes a discussion between you and your payment provider.

Apple Pay is not involved in any of this, beyond being a convenient way to use your payment cards.