Try first to free up iPhone device storage see this Apple articles below:
If you need more space for an update on your iPhone, iPad, or iPod touch
If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support
How to check the storage on your iPhone, iPad and iPod touch
How to check the storage on your iPhone, iPad and iPod touch – Apple Support (UK)
Clear Other storage on your iPhone or iPad
Clear Other storage on your iPhone or iPad - Apple Support
What's the difference between device storage and iCloud storage?
What's the difference between device storage and iCloud storage? - Apple Support
Then check the range of the mobile network, see this Apple article: If you see No Service or Searching on your iPhone or iPad
If you see No Service or Searching on your iPhone or iPad - Apple Support
Check also the Wi-Fi network, see the following Apple articles:
Connect to Wi-Fi on your iPhone, iPad, or iPod touch
Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network
If your iPhone, iPad, or iPod touch won't connect to a Wi-Fi network - Apple Support