I have some game purchases my kid made with out my permission and I need a refund on them

1.

If the invoice has to do with an app that has a subscription associated with it, see -> Delete apps on your iPhone, iPad, and iPod touch -> Delete apps on your iPhone, iPad, and iPod touch - Apple Support

• If you delete an app, it doesn’t cancel in-app subscriptions that you might have. While deleting an app, you might see a Cancel Subscriptions option. Learn how to cancel your subscriptions.

If you don't want to continue a subscription you need always to cancel that subscription in time, see the following Apple articles:

If you want to cancel a subscription from Apple

If you want to cancel a subscription from Apple - Apple Support

If the subscription that you want to cancel is not listed

If the subscription that you want to cancel is not listed – Apple Support (UK)

2.

If you have received an invoice from Apple, on every invoice from the Apple Store and/or iTunes Store always states what you have purchased (and/or concerns a subscription) and the amount.

Tap on Report a problem on the invoice.

Or try to ->  Request a refund for apps or content that you bought from Apple.

Request a refund for apps or content you've bought from Apple – Apple Support (UK)

If you have requested a refund, you must wait until Apple has approved. Then you will receive a message from Apple.

Refunds are not guaranteed. For more information, see the Terms & Conditions.

3.

To avoid the case in the future, see:

Require a password for App Store and iTunes purchases

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 (UK)

Prevent in-app purchases from the App Store

Prevent in-app purchases from the App Store – Apple Support (UK)

Click here for more support and assistance.

Here's how to request a 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 ].

If you are letting children use your equipment, read this support article: Require a password for App Store and iTunes purchases - Apple Support