In potentiostat (3 electrodes system) of electro-chemical, I need to apply negative voltage range from -1.50 to -0.30 (up to 50 mA range) as a source power to electrode and that negative voltage must be very precise and accurate.
I want to use output pin of arduino uno but I did not getting ideas that how to implement it by arduino uno board.
"Very precise and accurate" does not usually apply to the Arduino. The "analog" output is PWM, which is great for driving motors and LEDs but not great for other things, like yours.
The easiest method of getting a "negative" voltage is to attach the "zero" pin of your electrode to +5V and then regulate some voltage less than 5V (like 3.5 to 4.7) so that the electrode sees the correct negative voltage. This only works if there is no other connection between the systems, like is this electrode in a conductive container which is earthed?
50mA is also a little above the basic Arduino pin drive capability. A Teensy has a 12-bit true analog output but it's limited to 25mA on any digital pin and I can't find the current limit for the analog pin.
So you're definitely going to need some external amplification to get to 50mA, plus either a DAC chip or some filtering on a PWM output.