Can’t log in

Is it the same Apple ID you used to sign in here? If not, where are you trying to sign in when you have the problem. Note that there have been quite a few server issues lately. For starters, see If you can't connect to the App Store, iTunes Store, or other Apple services https://support.apple.com/en-us/HT201400. Among other things, in the above document, see Check Apple’s System Status page. You can check there to see if the needed server is available when you need to use one. 

Some other things you can try. Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Backup - Restore your device from an iCloud or iTunes backup.