Apple refuses to refund charges made by minor

If the child has their own device, they need their own Apple ID, which is managed by you through Screen Time and/or Family Sharing. If for Apple Pay purchases, they should not have your PIN number, since giving out your PIN is also authorizing purchases made with it.

When the child is set up with their Apple ID, you have many options for how you authorize purchases made by them, with the most common being part of the Family Sharing plan that gives you the "Ask to Buy" option when a child wants to make a purchase.

Approve what kids buy with Ask to Buy - Apple Support

Setting up Screen Time is also a way to prevent purchases. This can be used on your device or theirs. On your device, you can turn on Screen Time at any time to restrict purchases and many other things that a child should not have access to.

Prevent in-app purchases from the App Store - Apple Support

If they know your Apple ID Password, change it now. Giving them the Password is authorizing them to use it.

Change your Apple ID password - Apple Support

If you need to change your Passcode, do that as well.

Set a passcode on iPhone - Apple Support

Keep your Password/Passcode information private and never give it to anyone. If you give it to anyone, then you are authorizing the purchases they make. Purchases cannot be made without the Password/Passcode.

Hello ~ In addition to the excellent advice given by *Mac Jim ID* we are fellow forum members like yourself and have no authority to reverse any decisions made in your situation. Also Apple has no way of knowing that you aren’t making the purchases yourself and expects us all to keep our devices protected. I am sorry you find yourself in this position and this is an expensive learning experience. Take care. Also…

Require a password for App Store and iTunes purchases - Apple Support

~Katana-San~

If the child is sharing your Mac, then Screen Time must be set up there as well. Not only does it prevent Account Changes and App Store purchases, but also prevents them from viewing explicit web sites and from communicating with unknown people. This is set using a PIN number that you provide and when you use the Mac, it can be easily shut off after entering the PIN number. You would just need to turn it on when your child is going to have access to it.

Use Screen Time on your Mac - Apple Support