How to get a refund for a purchase my child made?

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

You must do it yourself. Nobody on these forums can make a refund request for you.