Is there any restriction on Officer employee union filing writ petition on behalf of an Officer employee?

You are the aggrieved party. only you have to file the case.  Your union cannot be said to have been affected.  Union has no locus standi.  However Union can also be a party along with the affected person(s).

File a review petition drafted by an expert advocate on punishment imposed.  I am sure that management may at the most warn and reconsider their severe punishment.

Unless you exhaust the laid down process, it is not proper to approach the Court.  Also consult with the All India Association and let them use their good offices for reduction in severity of this punishment.

Only for not joining the new promoted post, no management can take such severe step and there may be some other serious reasons.

Whether it iis a private bank or PSU, you have not provided information.

I'm from PSU bank only. My increments were stopped for not accepting the promotion only. No other issue. Thanks for the reply. Why a Union cannot file a case on behalf of it's member.
My point is, Union takes care of it's member when some injustice happens to him by the management by raising the issue with management. If the management is adamant in listening to the legitimate request of the Union, why a union, on its own file a writ against management as it's very purpose of running the union is getting defeated by the adamant management. Is union not at all aggrieved in this case..? What prevents the court in accepting the writ by an aggrieved Union ?

In your original post, you wanted to be enlightened.

Now I realise that even from the very beginning you are highly enlightened.  

Try your luck.