Is it possible to receive a refund on app purchases that were made by my child after the 90 days?

After 90 days not sure, but you can always try.

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.

. . . that were made by my child

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)