How can I cancel my payment or Apple billing?

After a purchase is made by double clicking the side button followed by verification with FaceID/Passcode, it cannot be cancelled. Subscriptions can be cancelled, but that only prevents it from being renewed, it does not make the initial transaction go away. If you owe money that has not been paid, you will not be able to download any apps until the previous purchase has been paid.

If what you mean is how do you remove a payment method, or what to do if you can't remove your last payment method or use no payment method with your Apple ID, read this article ➔ Remove a payment method from your Apple Account - Apple Support

Unexpired subscriptions, outstanding balances and Family Sharing organizers must always have a payment method present. To edit the cards used for those you may need to first add the new card and move it to the top payment method position before removing the old card (see: If you need to change or update your Apple Account payment method - Apple Support ).