I often face this issue. The fingeprint sensor does not work and sometimes the touch also misbehaves when phone is charging.
Why does this happen and how to fix this?
I experienced this issue with Mi Note 4, as well as Redmi 4A.
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As requested by OP posting answer, in response to my comment (now deleted) based on my experience
Having a clean power supply, using original charger + USB cable, setting up finger prints again are the common things that work...
I am not sure as to why touch sensor works only with original charger but posting as it may help, as it helped OP
Don't know the exact answer but from my experience It seems that touch sensors are finely tuned and calibrated against voltage reference. Using power supply other than provided chargers might be affecting these calibrations and cause fluctuations that results in malfunctioning of touch screen - that is - we click on something and something else is clicked or sometimes touch doesn't work, etc.
Something I have noticed with my fingerprint sensor is that if phone is face down and hasn't been used for a short while, phone will not read finger print until phone is actually picked up. Not sure if because of proximity or orientation sensor, but appears to be that way to keep from accidental unlocks. Is your phone face down when attempting to unlock? Also, what do you mean by "touch misbehaves"? If you mean the entire touchscreen and then combined with fingerprint sensor this could be pointing to your device being defective.