iPhone showing App Store problem

What is the exact message (it helps to be precise here)?

Here are a variety of resources helping with connectivity issues:

Restart your equipment and/or sign out and back in again, and try again.

If you can't connect to the App Store, iTunes Store, or other Apple services, read this support article --> If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support

Here's a related article about what to do if you can't connect or sign in to iCloud --> If you can't connect or sign in to iCloud - Apple Support

If your iPhone or iPad won’t connect to a Wi-Fi network, or if you have related connectivity issues, read this support article --> https://support.apple.com/HT204051

Here's a case where using a VPN prevented sign-in --> AppStore - Apple Community

Remove the VPN entirely, don't just turn off.

If none of the resources provide a solution, contact Apple for assistance:

For support, click here --> https://support.apple.com/choose-country-region Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service --> "See a list of Apple phone numbers around the world."

Click here --> Contact Apple Support - Apple Support

It may be a temporary server side issue, although there are no problems noted on the System Status page and I currently have no problem accessing it on my devices. More tips are available here:

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

Does the message say "Can't Connect" or something else that may provide more information?

Are you using a VPN? If so, it should be removed.