Ohm's Law in Practise
I just measured the voltage at the end of this AUX pin(No load is connected) approximately 2mV using a DMM .
  But when I measured the current, it didn't indicate any current in the DMM.


By Ohm's Law

$$I = \frac{V}{R}$$

If you didn't connect any load, then \$R\approx\infty\$. Therefore, no matter what the voltage is you expect \$I\approx0\$.

In general, an ideal open circuit can sustain any voltage without passing any current. In practice, if there is air between the unconnected wire terminals, there is some limit to the voltage before a spark will be generated to carry charge between the terminals.