How do I get a refund for an unauthorized purchase by my child on my Apple Account?

Here's how to request an app or media refund from Apple (From: https://support.apple.com/HT204084 - see the article for more detail.) If you bought this in the EU from a third party, see: https://support.apple.com/118126 instead.

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 --> https://support.apple.com/118428

Read this support article for information about how long it takes to receive a refund (if you are granted one), and how to check the status of a refund for apps or content that you bought from Apple --> https://support.apple.com/HT210904

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 ➔ https://support.apple.com/HT204030

or

On your device you can use Screen Time to prevent unintentional or unauthorized purchases from the App Store, in-app, and other Apple services. —> https://support.apple.com/102470

or

Use Guided Access to permit a person to only use a single app —>

https://support.apple.com/guide/iphone/use-guided-access-iph7fad0d10/ios

All you can do is try by using the link here:

Request Refund

You have authorized anyone to make a purchase when you give them the Passcode to the device. Once you do that it is up to you to prevent them from making purchases and there are many ways to do that.

• Require a separate password for purchases

Require Password for Purchases

• Prevent in-app purchases

Turn off in-app purchases

• Use Parental Controls to remove the App Store

Parental Controls

• Use Guided Access

Guided Access

If you got an email receipt and there's a 'Report a Problem' link in it, use that; otherwise, click here and ask the iTunes Store staff for a refund.

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Just to be clear, none of us work for Apple or have any ability to review a request. We are simply other Apple users who volunteer our time and experience to provide assistance when possible. It has been observed that you will only get one chance to appeal after an initial denial. Even though Apple states that All Transactions are Final in the Terms of Use for your Apple Account, at times Apple may provide a compassionate refund on a case by case basis, but it should never be expected.

Since we have no control over the decisions made by Apple, all we can do is help you prevent that from happening again.

If it has been denied twice then I very strongly suspect it will continue to be denied, if not ignored altogether.