Separating Apple ID
Solution 1:
Welcome to Ask Different. You can create a new Apple ID for your child the same way you created one, here's a good walkthru you can follow.
When your son signs in under the new ID, they will not see (and thus they will lose) any content or game progress they made under your ID.
You should also decide if you want to do Family Sharing. Here's some info about that. This will allow you to use Apple's parental controls for your son. If this interests you, I would recommend reading this article before you setup your son's new ID.
Solution 2:
If your son signs out of the AppleID on his phone, there are options to keep most settings on the phone. This works for Contacts, Calendar etc, but there are a few exceptions such as Notes.
Applications should remain, but will not be able to be updated, unless signing in to the AppleID used to purchase them. You can enable Family Sharing on your AppleID which will let the phone be setup for app purchases. Family Sharing does have some privacy aspects which your son may find unacceptable.
He would then have to create a new AppleID (or sign into the new AppleID you created) on his phone.
I have just been through the process of changing from one AppleID to another, and it can be a difficult process. The most time consuming task was updating apps - if these were purchased under the old AppleID (even if "free") they need to be deleted and reinstalled under the new. This should not be necessary if the old AppleID is now used for Family Sharing.