Cannot connect to App Store via iPhone - Wrong Password although password is right
If the servers are broken or the network isn't working between you and the servers, your password isn't actually wrong. Even when all lights are green at http://www.apple.com/support/systemstatus/ it could be an issue that'e exclusively server side, and you'll need Apple Support to get to that conclusion.

Barring that, you can certainly to go through "the usual troubleshooting steps" on iOS since you're unlikely continuing to type the password incorrectly.

You should start with the support article below:


https://support.apple.com/en-gb/HT203005


Before you contact support (the link at the bottom of the page - the next step if that doesn't work) is to maybe try a restart. Since the app store needs an accurate time and date:


Sign out of the store from preferences
Turn off "automatically set time" in the settings app, General, Date &amp; Time
Put the device in Airplane mode
power off the device and maybe go make some tea while it powers itself off
When you start it up again, set the clock manually to within 10 seconds of a good time source and then enable WiFi or cellular data as you please.
Try to sign in to the Settings App - iTunes &amp; App Stores section
After one failure, turn on automatic time setting
Try to sign in to the App Store