circuit triggers with bad voltage 0.05v
what is the issue or alteration to be done to fix the circuit to work only at 0.5volt or higher is applied on the signal pin

A overall more sensible topology for what you are trying to achieve.  The PNP front end references its input to the 12 V supply. Setting it up to threshold at 500 mV is going to be tricky since that really means 11.5 V from the transistor's point of view.  A 10% error in that threshold changes it by over 1 volt.

Either use a comparator, or at least a NPN front end.  If you can live with 600-700 mV or so threshold, then you can use the B-E junction in the transistor as the comparator.

You may also need to invert the logic, depending on what you intend to "work" when the input signal is above 500 mV.