Hi AndriStar,
It sounds like you're looking for help updating your iPhone. We're glad you've joined us in Apple Support Communities. Let's see if this helps.
Follow the steps in If your iPhone, iPad or iPod touch won’t update. This link has the most frequent solutions to troubleshooting when your phone won't update. In your case, you'll want to pay special attention to the sections, "If you can’t reach the update server or can’t verify the update" and "Remove and download the update again."
Double-check that your Wi-Fi has a checkmark next to the network and if it doesn't follow the steps in: If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network. If it does have a checkmark, you'll want to try a different Wi-Fi network.
If you complete the advice from the above links and you still can't update, then let's try to Update your device using your computer. It will guide you to update with a computer if you can't update your iPhone wirelessly.
If the issue remains after following those steps, let us know what steps you had a chance to try and what happened when you tried on another Wi-Fi network.
We hope that helps with your question and take care!