When I try to update my iPhone I get a message that I’m not connected to internet. However, I am connected to the internet.

See this for some help. It is a User Tip prepared by one of the senior users here on the ASC. Updating iOS: common issues and solutions - Apple Community

Not knowing the exact error makes it difficult. However, see if this helps, If you see an Update Failed or Apple Pay Not Available alert after iOS update or restart - Apple Support or provide the exact error message you are seeing, or a screenshot would help as well. Just remember if you do post a screenshot to block any personal identifying information.

Did you follow the steps in the What To Do Next section of the link I provided? If you did and it is still not working, then you need to contact Apple Support. Use the Contact Support link at the top of the page here to start a support request.

Are you trying to update over the air, directly from the iPhone? Are you using a stable wi-fi network?

Thank you for the quick reply. When I go to cellular in settings, it says error>. When I click error it says “An update is required to use cellular data on this phone”. When I click learn more, it takes me to the link you just provided.

I was able to use this guide to download iOS 14.4 BUT it still won't connect to cellular service. It still says I need to update my iPhone. Any help would be greatly appreciated.