My iPad always display “Unable to verify update iOS 12.5.5 failed verification because you are no longer connected to internet” even I have internet connection what will I do

Your WiFi router may be unexpectedly blocking access to some internet resources or servers - this is not uncommon with NAT routers. So as to eliminate this as possible cause, the router should be restarted.

To restart your router, disconnect power from the router for at least 30 seconds - then reconnect power to restart. After your router reboots (which may take several minutes), force restart your iPad as before:

• On an iPad with a Home button: Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On an iPad with Face ID: Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top button. When the Apple logo appears, release the button.

You may also have a DNS problem. If the problem persists, I recommend that you manually set your DNS settings (for your iPad, Router, or preferably both) to use one of the following services - for which IPv4 and IPv6 server addresses are listed:

Quad9 (recommended)

9.9.9.9

149.112.112.112

2620:fe::fe

2620:fe::9

OpenDNS

208.67.222.222

208.67.220.220

2620:0:ccc::2

2620:0:ccd::2

Cloudflare+APNIC

1.1.1.1

1.0.0.1

2606:4700:4700::1111

2606:4700:4700::1001

You may have been connected to a unreliable wi-fi network; connect to faster, more reliable WiFi and try again.