Recently I had a screen time passcode setup on my childs device, i do not remember the passcode or the apple id linked to it what do I do?

For Problems With Your Apple ID

1. Forgot iCloud Password
2. Forgot Apple ID
3. iForgot Password - Apple ID
4. iForgot UserName - Apple ID
5. Apple ID Password Change
6. Apple ID Name Change
7. Apple ID - Apple Support
8. Manage your Apple ID primary, rescue, alternate, and notification email addresses
9. About your Apple ID email addresses
10. Get help with Apple ID
11. Contact Apple for help with Apple ID account security - Apple Support
12. What to do after you change your Apple ID email address or password - Apple Support

Reset Security Questions

Contact Apple for help with Apple ID account security

If you forgot the answers to your Apple ID security questions - Apple Support

You may need to reach Apple’s Account Security department. If you cannot find your country or are not able to call, then complete this form and send it to them.

Try using Apple's iForgot service. If it says they don't have sufficient information, you need to contact Apple's Account Security team. To reach them, click here and pick a method; if you can't use any of the ones listed, fill out and submit this form.

If you forgot your Apple ID password https://support.apple.com/en-us/HT201487

You also can use Having trouble signing in/iForgot https://iforgot.apple.com/password/verify/appleid 

And you will need to see If you forgot the answers to your Apple ID security questions https://support.apple.com/en-us/HT201485

Before trying to answer your security questions is very important that you think about your questions, including your birth date, and their answers carefully and try to recall all details you can. If you don't answer them correctly enough, then you easily can lose control of your account.

Screen Time passcode reset