Why does my authentication code keeps popping up on my iPhone 7 Plus & how to get rid of that icon?

Check the steps provided in these support guides:

Two-factor authentication for Apple ID - Apple Support

or

Get a verification code and sign in with two-factor authentication - Apple Support

If nothing changes, please contact Apple Support again, using the link I gave you in my 1st reply.

If you get no help, I would make an appointment at your most convenient Apple Store or Authorized Service Provider asking for their help. See this list: Apple - Find Locations - Location Selector

Regards

Giulio

Hi

Go to appleid.com turn off 2 step verification then turn back on again.

You may get verification code one more time.

Go to books download ios 11 user guide & iPhone 7 guide both are free.

Cheers

Brian 🇬-1F1E7;

Contact directly Apple Support and explain your problem. Use this link:

Contact Apple for help with Apple ID account security - Apple Support

Regards

Giulio