FWIW, you should never have shared an AppleID; separate AppleIDs are essential to proper functioning of all iOS features.
Make sure that each family member has a unique Apple ID - Apple Support
But that’s now water under the bridge.
You first need to completely “wipe” your info from your child’s phone by carefully following ALL of these steps in-order:
What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support
THEN you can setup your child’s phone with his own AppleID. (Don’t delegate this initial setup to the child … they only “think” that they’re adults)
Pay VERY close attention to carefully setting-up Parental Controls:
Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support
Restricting the child’s ability to change the AppleID and device Passcode are IMO essential elements to maintaining effective parental oversight.