Q: My iphone6 cannot update and I still have IOs 8.1.3 version. When I click checking for update it will never complete checking so what to do to update it and my fingerprint id is also not working

Hi.Check these articles:

If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support

Get help with iOS update and restore errors - Apple Support

Have you tried updating using iTunes instead of Over the Air? It is a better way to update and may allow you to complete the process. Connect your phone to a computer, open iTunes and on the Summary page select Update.

Regarding your fingerprint ID it could be software or it could be a defective phone. Try this first, a forced restart. Hold down the Home and Wake/Sleep buttons at the same time for about 15-20 seconds until the Apple logo appears. Ignore the "Slide to power off" text if it comes up. You will not lose any data or apps.

If that does not work, I would take the phone to an Apple Store to check it out.

Good luck,

elcpu