If you did not purchase it from the website, then Apple can manage the subscription and you can find it here:
If you want to cancel a subscription from Apple - Apple Support
then requesting a refund is done through Apple here:
Request a refund for apps or content that you bought from Apple - Apple Support
I suspect though that you bypassed Apple's ability to manage the subscription and purchased it directly from their website. Apple Pay just securely transmits your card information to the merchant. You cannot request a refund or cancel a subscription through Apple Pay. You will need to contact the website to get your subscription cancelled to avoid further charges and you can also see if they will provide a refund. Any refund will go directly to the bank that issued your card used to pay for the subscription. Refunds do not go to Apple Pay.
Disputing charges is done the same way whether Apple Pay was used or not. You would dispute a charge with the credit card that was used for the transaction. Apple Pay is not a bank where charges are disputed.