Unable to log into App Store on my iPhone 4 using Apple Account

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 --> If your iPhone or iPad won't connect to a Wi-Fi network - Apple Support

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

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

For support, click here --> Choose your country or region - Official Apple Support 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 for support and service - Apple Support

FYI: Even if you manage to get logged into the App Store, you’re not going to find much of anything in the way of apps that are still compatible with the iPhone 4. That device is long obsolete and isn’t even usable as a phone in most of the world any more.