If something goes wrong with your iPhone and you need to restore it, booting into recovery mode is a highly recommended way. Here's how to enter recovery mode on your iPhone 6s and do an iPhone system restore if you need some assistance:

1. Connect your computer to the USB cord, but not the iPhone.
2. By pushing and holding the Power button for a few seconds until the slider appears, you can turn off your iPhone.
3. To turn off the gadget, slide the slider to the off position.
4. Wait for the iPhone to totally shut down. You may also press and hold the Power and Home keys at the same time. Release both presses when the phone shuts off.
5. Connect the USB cord to your iPhone while pressing and holding the Home button. The gadget should now be operational.
6. Hold the Home button down until you get the Connect to iTunes screen. When that screen appears, press and hold the Home button.
7. After that, an iTunes popup should appear, informing you that your device is in recovery mode and that you must restore it.
8. To restore or update your iPhone, follow the onscreen instructions. It's possible that the restoration of your iPhone will take longer than expected, so be patient.

If the blue screen reappears after the restoration, it's very certainly due to hardware failure. The motherboard or some components of the iPhone may be damaged, necessitating repair.