INA212: Minimum measurable current

Anand, 

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The reason for this behavior is that there are several error factors that become more prominent when attempting to measure smaller currents, the largest of these being voltage offset and input bias currents. Have a look at these values from the INA212 datasheet:

First, the offset voltage will be present on the shunt in addition to the generated sense voltage, and contribute a proportional amount of error. This means that the generated sense voltage needs to be large enough with respect to this value that the error is acceptable, but eventually, as the signal of interest becomes smaller, this error source will begin to dominate the measurement. 

The second portion, Ib, is a current that it present on the line a part of the cost to operate the input bias stage of the amplifier. The portion of this entering the negative input of the amplifier will also pass over the shunt, and therefore this is added to the measured current. As such, if you are attempting to measure currents in the 10's of uAs, I would advise against this device for this very reason. Here is what the error curve of your current setup looks like from 100ua to 100mA:

For measurements of this magnitude, I would recommend having a look at INA190 or INA186. These devices have an input bias current in the nA-pA range, and are much better suited to this range of measurement.