This sounds like a problem with the motor itself. Or, maybe the power supply is malfunctioning.
Merely having a power supply that is capable of providing more current than is required isn't a problem because the load will determine how much power it draws.
So the answer to your title question is that you can reduce 12V16A to 12V3A by making sure your load doesn't try to draw more than 3A.
Time to break out the multimeter and watch the voltage into the motor and see what is happening. Or try a different motor to try to localize the problem.
If it looks like the problem is the power supply, then you can confirm by using a lab-style bench power supply to run the motor.