"Cannot verify server identity" pop-up on iPhone screen

Your may have a subscribed Calendar or a CalDAV or a CardDAV/LDAP account for Contacts or Calendars.

What happens when you click the "Details" on the error popup message (See the Pic below)

The best would be to Delete and Add the email account that is creating the issue.

You may also try changing SSL settings

Settings > Password & Accounts > [Select the Mail account} > [Tape on Account with the email ID} > Advanced > SSL Settings > [Disable]

Click <Account (in Blue)

Click on DONE (in Blue) when exiting in the previous screen

Probably you may have accepted an offer or subscribed for a spam Calendar accidentally. Watch the GIF below to know how to unsubscribe from these calendars. Look for an unknown Calendar on the device under subscribed calendars.

The pic below is self-explanatory if you have subscribed to a calendar.

Delete any subscribed calendar you don’t recognize:

• Delete calendars and events on iPhone - Apple Support

and test again.

"'Cannot verify server identity' pop-up on iPhone screen"

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Cannot Verify Server Identity:

There is an issue with the SSL (encryption) of an open app --most likely a mail app.

A. Close All Apps:

Cave what need be, and then close all apps. Hold you finger down as you swipe up form the bottom-left corner of your screen. Then, close all of these open apps, by sweeping up quickly for all apps.

B. Perform a Force Restart:

Try Force Restarting your iPhone. Save any information that need be. Then perform the restart. See if you can then perform this. Go Here: Force Restart iPhone - Apple Support

C. Add the eMail Account Back:

Whichever app you are using for Mac, remove the gmail account, then then add it back.

D. Reset your iPhone Settings:

1. Go to: General
2. Tap: Reset
3. Tap:  Reset All Settings
4. Use: your passcode (if prompted)

As a Last Resort:

E. Reset your iPhone to Factory Settings:

If you just can't get out of this, then you'll have to reset your iPhone to Factory Settings. Go Here: How to Factory Reset your iPhone, iPad, or iPod touch - Apple Support. Much would be lost, if you don't backup anything.