You can file a writ petition in this regard before HC not it's difficult to get promotion with retrospective effect

Notional promotion is permitted with retrospective effect. If a wrong is done, consequential benefits must be
given on notional promotion.

1. Your query is incomplete to formulate an opinion.

2. Are you a public servant?

3. If notional promotion has not been considered or if promotion has unjustly been denied then a writ petition can be filed in the High Court.

Advise above is court observation in ruling.

If you are aggrieved by the decision of the management in respect of yor promotions which are delayed for no fault of yours, you may first make a representation in writing to the top authority through proper channel.

If the authority is not responding in a favorable manner or your efforts within the department do not yield fruitful result then you may plan to approach state administrative tribunal or central administrative tribunal with a OA on this seeking relief and remedy.

There are many judgement, you can browse  through google search in the legal online websites namely indiankanoon.org or livelaw.in or lawweb.com etc. 

If your service rules entitle you to put in such a
claim that your promotion benefits have a
retrospective effect then you can claim such
benefits.

1. Yes you can fight for promotion with retrospective effect. 

Notional promotion is the only remedy available for you along with increase in pay. Therefore give a representation to that effect and then if they do not respond file a case.

Engage a lawyer who will give judgements to the court when required. This is a settled issue.

1. As per the information mentioned in the present query, makes it clear that you have been denied the promotion on the fault of many unwanted reasons.
2. Yes, you can very well ask for the same prayer before the court of law.
3. You can file a Writ Petition before the Hon’ble HC of Mandamus in nature seeking direction for the them to consider your case.