Hi TejasTrenton,
Are you using Screen Time for yourself?
Or are you using the child's iPhone to test, but you have another iPhone as the adult?
If you are using Screen Time for yourself, it does work a bit different, as shown on this page:
Set up Screen Time for yourself on iPhone - Apple Support
We also noticed that you show that your iPhone is using iOS 12. An iPhone X has the capability to be using the newest iOS 16 software.
Screen Time was introduced with iOS 12, and there have been changes and improvements since then. We'd advise to back up and then update your iPhone X to take advantage of all that Screen Time has to offer.
Update your iPhone or iPad - Apple Support
You may need to update using a Mac or PC, as this is a large update from iOS 12 to iOS 16. The directions to follow depend on which macOS versioning your have, and if you're using a PC.
Mac with macOS Catalina or later: Update your iPhone, iPad, or iPod touch with the Finder - Apple Support
Mac with macOS Mojave or earlier, or a PC: Update your iPhone, iPad, or iPod touch with iTunes - Apple Support
Take care!