I think you could use an external pot connected to A2. If you make a voltage divider using another resistor, then the resistance of the pot will determine a smaller voltage range.
For example: connect the 5V source to 30K or 40K of resistance, then to the left lead of the pot. The middle lead of the pot goes to A2. The rightmost lead of the pot goes to GND. This way, the full range of the pot will provide 0V – 1V to A2 and this will allow finer adjustment.
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