Hello Vkgupta2812,
It sounds like you aren't able to complete the pairing process to your Apple Watch due to an error that states that you are not connected to the internet.
If you haven't already, let's have you update your iPhone to the latest iOS: Update your iPhone, iPad, or iPod touch
Make sure that the date and time are correct on the iPhone.
Press and hold the Digital Crown and then select Reset to reset the Apple Watch.
Check the iPhone Settings > General > iPhone Storage for an Apple Watch software update. If one is found here, swipe left to delete it.
If there are any Bluetooth accessories connected to the iPhone, temporarily disconnect (not unpair) them.
Forget the Wi-Fi network that the iPhone is connected to and then reconnect to the Wi-Fi.
Go to Settings > General > Reset > Reset Network Settings. This will reset your previously connected networks and their passwords, cellular settings and nay VPN/APN settings you may have used before. So you would need to enter that information back in.
Try setting up the Apple watch as new instead of from a backup.
Regards.