ADC is giving fault codes when I touch thermistor attached to it
You need to ground the shielding (sheath). This is what keeps you from capacitively coupling noise into your high impedance inputs. Ground reference to the ADC is important. If you don't ground the ADC circuit board, at least put a 1 MOhm resistor to ground to provide some reference.
Edit: There may not be a good reason to keep your digital and analog grounds separate since the analog and digital VDD are the same. The shielding of your probe should be connected directly to the analog ground. Still, if you want the isolation, put the 1 MOhm between the analog and digital grounds.