iOS 15.7.1 unable to verify update

Check your WiFi Router / Modem for --> Recommended settings for Wi-Fi routers and access points ...

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

I have the very same problem. I have downloaded the ios 15.7.1 update but I get the "not connected to the internet" message when I try to install. I am connected to the internet via wifi with a strong signal - but I also have a strong cellular signal to connect. Neither works. This is clearly an Apple bug.

I have the same issue with iPadOS 15.7.1. I've tried all of the suggested remedies, such as resetting network settings, deleting the download and redownloading, doing it all over cellular (Wi-Fi disabled), doing it all over Wi-Fi (cellular disabled), trying five different Wi-Fi networks, etc. I'm stuck.

This is on an iPad Pro (11-inch), MU1D2LL/A, running iPadOS 15.7.

Found my issue, so in case this helps others: look for a beta profile in Settings > General > VPN & Device Management. Deleting that profile fixed my issue.