Dear Yavuz,
okay, then it seems like we need to dig deeper to find the root cause for this issue. However currently I do not know where to start. Can you describe exactly how the output code changes or what you observe when the device is misbehaving?
What exactly happens when you are outside the allowed common-mode voltage range is hard for me to quantify. I would assume the linearity of the ADC degrades and maybe you measure a smaller signal than it is in reality.
I don't know what kind of signal or sensor you have connected to AIN6. But if you can measure this signal with respect to AVDD/2 then this would certainly be an option. You probably only need to do the math in the MCU then.
So you would connect Vbias=AVDD/2 to AIN7. However this is not a very stable voltage as it changes with the supply voltage. Your measurement result would therefore not be very accurate.
A better option would be to route VREFOUT to AIN7 and then measure AIN6 with respect to VREFOUT.
A 3rd option I could think of - this depends on the kind of sensor you are using - is to bias/level shift the sensor and AIN7 to Vbias. This would work as well if the sensor supports it.
Regards,