iTunes iPhone 7 plus

You might like to do a force restart of your iPhone using the steps below ( a force restart will not delete any settings or data ).

• On an iPhone 7 or iPhone 7 Plus: Press and hold both the Sleep/Wake and Volume Down buttons for at least ten seconds, until you see the Apple logo.
• On an iPhone 6s and earlier, iPad, or iPod touch: Press and hold both the Sleep/Wake and Home buttons for at least ten seconds, until you see the Apple logo.

Allow your iPhone to reboot then go back to Settings > iTunes & App Store and again try to sign in with your Apple ID details.

Ok it might be worth contacting Apple Support using the link below or by visiting your local Apple Store and have a chat with them and see if they can assist to resolve this issue.

Contact Apple for support and service - Apple Support

For the iPhone, you use Mac's iTunes app to download iPhone apps

See your account: iTunes > Account > View My Account... > sign in

Mac App Store is for Macs, apps from the Mac App Store do not run on iPhone.

You could try the following on your iPhone.

Settings > iTunes & App Store and if it shows your Apple ID at the top in blue tap the Apple ID and then tap Sign Out.

Then restart your iPhone and go to Settings > iTunes & App Store and sign in with your Apple ID details.

Now open the App Store app, you might be asked to sign in with your Apple ID when downloading or purchasing your first app.