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Hi Pawel,
On this part, we have the internal op amps that can be used to gain the signal to do current measurements. See figure 5-3 on our MSPM0 Gauge L2 Solution Guide pay special attention to the 20m ohm resistor.

Otherwise you can use any ADC channel instead of the OPAs, use a similar method of ADC input on both ends of the resistor. From the ADCs, you can measure the difference (drop) across the resistor. The GND connection would probably be best on board ground (or if you have a ground source from the voltage input) and make sure its a solid ground connection.
Make sure not to have any fast switching signals that could couple onto your ADC readings (low-pass filters can help reduce observed thermal noise).
Regards,
Luke