I can't proceed with my IOS update. it says Veirification failed because I am no longer connected to the internet, But I am connected with out WIFII. What must be the problem?

Connecting to Wifi is the first part and then getting connected to the Internet is the second

1. If you connect to Wifi, doesn't necessarily mean you are connected to the internet. If you are not connected to wifi could be a problem with iPhone settings or Router/Modem Settings
2. If you are not connected to the internet is the sole issue of Router / Modem Settings. Contact your ISP immediately

For your Internet connection.

• Over Cellular: contact your Carrier (Cellular Service Provider). The agency who issued the SIM to you
• Over WiFI: Contact your ISP (Internet Service Provider), the agency who provided the Internet Service on your Modem/Router to you

However --> Connect iPhone to the Internet - Apple Support