My App Store is not working

See these Apple articles below:

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

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

If you can't connect to the App Store, iTunes Store, or other Apple services

If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support

-> If you tried all of the above steps and you still can’t connect, contact Apple Support.