forgot the screen time password we set up for our sons phone and now cannot change

You can only change a screen time password on a device which is on iOS 13.4 or higher. Your signature suggests you have an iPhone 5c which is on iOS 10.

If that is what you have you will have to completely erase the iPhone using your computer with iTunes and set it up again. You cannot restore from backup in this situation as the passcode is in the backup and it would put you right back where you are.

See the directions in this link --> If you forgot your iPhone passcode - Apple Support

If your signature is not correct and the phone is a newer phone with at least iOS 13.4, see this link --> If you forgot your Screen Time passcode - Apple Support Again, this will only work on a phone at iOS 13.4 or higher.

Wipe the phone, set it up as a new device.

Set the new screen time passcode.

Restore from your backup.

If the article linked above doesn’t work, you must erase the iPhone and set it up as new.