how is my child playing the xbox after his daily time limit is up?

The best solution would be to use the xbox gaming time as reward after your son has completed his daily chores and homework. You can do that easily by setting up screen time limits for your son, because believe me you can't keep a child away from the console.
To check how to set screen time limits: https://support.microsoft.com/en-us...ount-set-up-screen-time-limits-for-your-child

The Xbox app's profile (or profile on xbox one) for each user has time when people played a game last but I don't think there's anything that lets you see how long someone's played, except if you are a parent of a child account and you set screen time
limits:
https://support.microsoft.com/en-us/help/4028244/microsoft-account-set-up-screen-time-limits-for-your-child

There is a whole support page on how to place time limits on an xbox child account, just google it up.

Hi, this is a link on how to set your child's privacy setting

https://enforcement.xbox.com/en-US/home/howto#sub-topic2-2

Here is how to set up your child's spending limits

https://enforcement.xbox.com/en-US/home/howto#sub-topic2-3

And this is how to set a time limit for your child account

https://support.microsoft.com/en-us...ount-set-up-screen-time-limits-for-your-child

And here's how to add a child's account to your family account

https://support.microsoft.com/en-us/help/12417/microsoft-account-add-members-to-family

Hopefully those links will help will help with create your child's account. Be should to enter your child's birthday correctly because it can't be change.

Yes, I have child accounts set up - it wasn't necessary or on my radar when we first go the xbox as they were smaller and it was easy to limit their time/games. Now that they are getting older and can access the xbox without my help, I have set up child
accounts and researched how to set limits etc. The problem is that my one child has been playing a certain game faithfully and is devastated to potentially lose all his progress - and I would like to also protect myself and my own microsoft account/password
without having to give up that information to him. I hate that he will have to lose all his progress - even though just a game - so I can protect my own personal account. I was just hoping there was a way I could transfer over the gamertag to his account.
Thank you both for answering.