no connection to 4g after installing ios 15.1

Three basic troubleshooting steps to try (test your connection after each attempt):

A) A forced restart of your 12, using these instructions:--> Force restart iPhone – Apple Support

B) Reset your network settings going to Settings>General>Reset>Reset Network Settings, bearing in mind that this procedure also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before, but NO other data is affected.

C) Something could have gone wrong during the latest update procedure.

I would try to install a fresh copy of iOS/iPadOS. To do this, create a full backup of your iPhone/iPad (1), then restore it to factory settings (you need a computer to perform this step) and, in the end, set it up as new (2).

When done, restore data from your previously made backup (3).

Follow the instructions provided in these support articles:

(1) How to back up your iPhone, iPad, and iPod touch – Apple Support

(2) Restore your iPhone, iPad, or iPod to factory settings – Apple Support

(3) Restore your iPhone, iPad, or iPod touch from a backup

If the issue still persists, contact Apple Support directly using this link:--> Get Support or make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.