Your iPhone and printer are using a secure (i.e., encrypted) TLS/SSL connection.
Without delving into the technical complexities of TLS/SSL security, perhaps understand that each time your printer is restarted, it will generate and self-sign a new TLS Certificate to secure the connection. Self-signed certificates do not have a verifiable chain-of-trust that can be automatically verified; as such, as the Certificate cannot be automatically verified, you will see the warning that you report here.
The warning that you see is benign; accepting the warning causes your iPad to trust the Certificate until the Certificate time-expires (usually after, days, months or even years). If the printer is restarted, a new Certificate is generated; as the new Certificate differs from the previously trusted Certificate, you will see another warning.
Given that the warning is entirely expected, you can safely click-through and proceed to print.
As for your subsequent difficulty in successfully printing, this is separate issue...
If using a VPN connection, this may need to be disabled. VPN connections can disrupt AirPrint and other local network services. Similarly, if you have installed any "security" Apps (such as Norton or MacAfee), these can also cause issues; if these are installed, as a diagnostic exercise, they need to be removed.
Presumably your printer supports AirPrint; you may find that restart of your network components will resolve the problem. You’ll need to restart your network devices in the correct order. Assuming that your WiFi Router provides DNS services for your network, restart devices in this order - allowing time for devices to fully boot/restart prior to restarting other devices:
- WiFi Router
- Upstream wired Network Switch(es) (if any)
- WiFi Access Points / Network Extenders
- Other fixed infrastructure devices - such as Printers
- Client devices (your iPad)
Restarting your iPad, after restarting other devices in the correct sequence, is most simply achieved by a forced-restart of the iPad:
- 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.
If you continue to have difficulties, check to see if your iPad is using the new WiFi Private Address feature. This feature is intended to provide additional privacy and security when using “public” (untrusted) WiFi networks.
Settings > WiFi > [Your WiFi Network / SSID] - tap the “i” icon - Private Address
The Private Address feature is largely unnecessary for your home WiFi network; if enabled, Private Addressing can interfere with anticipated operation of other devices, such as AirPrint/Airplay. In such circumstances, you may need to disable this feature - and can be enabled or disabled for each individual network.
Use private Wi-Fi addresses in iOS 14, iPadOS 14, and watchOS 7 - Apple Support
