Need to fixate current of motor connected to a battery
An "80mAh motor" sounds rather unusual.  Are you sure that's what you meant?  A datasheet for the motor would be useful, but I'll assume you want to maintain 3V across it.

For a constant speed you need a constant voltage across the motor. Therefore you want a device that can convert varying lower voltages from the cell to a fixed higher voltage across the motor.

The solution is a boost converter. These are available in tiny packages around which you would design the necessary passives according to the datasheet recommendations.  Alternatively if you want a ready-made solution, you can also buy small boost converter modules containing the IC and necessary passive elements.

Note that you shouldn't do this in any situation where it's important to have warning of impending depletion of the cell or battery.