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"If you can't connect to the App Store, iTunes Store, or other Apple services" click here --> https://support.apple.com/HT201400
- If none of the suggestions work, try the last one: "If you’ve tried all of the above steps and you still can’t connect, contact Apple Support."
Verification Failed "problem connecting to the server" March 2018 - https://discussions.apple.com/thread/8321958 - Needed to connect over wi-fi and not through cellular.
And the opposite:
"Verification Failed, An unknown error occurred" March 2018 - https://discussions.apple.com/message/33184357#message33184357 - "tried again with Wifi off and it worked"
I'll note it does not seem you have wi-fi turned on at all and your cellular signal is weak. This could well be the reason you are seeing that message.