Are you using Family Sharing? Are you the organizer? What is Family Sharing? - Apple Support
If yes, the short answer is only one person, the Organizer, can (and must) have a card, but the Organizer can avoid having this charged by others by asking them to make sure they have adequate personal balance (e.g., from gift cards) to cover their purchases. Other family members can only pay for things by using their personal balance or by letting the remainder automatically roll over to the Organizer's payment method (such as a credit card but not the Organizer's personal account balance).
If you want him to cancel the purchase he will have to ask for a refund. You cannot do that for his purchases. Here's how to request an app or media refund from Apple (From: Request a refund for apps or content that you bought from Apple - Apple Support - see the article for more detail.)
1. Sign in to https://reportaproblem.apple.com
2. Tap or click "I'd like to," then choose "Request a refund."
3. Choose the reason why you want a refund, then choose Next.
4. Choose the app, subscription, or other item, then choose Submit.
If you were charged for a subscription that you no longer want, you can also cancel the subscription using the directions in this article --> If you want to cancel a subscription from Apple - Apple Support
This video will only tell you how to cancel a subscription on an iPhone ➔ https://www.youtube.com/watch/XXx-J-ueCtE
If you are having problems with unauthorized purchases being made on your device you may wish to always require a password for App Store and iTunes purchases.
Click here ➔ Require a password for App Store and iTunes purchases - Apple Support
Manage App Store purchases, subscriptions, settings, and restrictions on iPhone
Manage App Store purchases, subscriptions, settings, and restrictions on iPhone - Apple Support
"You can use Screen Time to prevent unintentional or unauthorized purchases from the App Store and other Apple services. You can require a password for purchases, prevent certain types of purchases, or disable purchasing completely." - Prevent in-app purchases from the App Store - Apple Support See how to 'Use Screen Time on an iPhone, iPad, or iPod touch' by clicking here --> Use Screen Time on your iPhone, iPad, or iPod touch - Apple Support
This could end up being a very long post if I have to cover eveery eventuality so why don't you tell us more about your purchasing setup such as family sharing yes/no, or does he have access to your equipment.