Mandamus writ

Already you collected the details about your game by Government authority and RTI that the game is not recognized sports by the National Sports committee. Therefore, instead of filing case you can submit all details related to the said game to National Sports committee with a representation to repaganize the sports. 

If the information collected by you through RTI application favour your case but the department do not agree to your claim / prayer what is the plea given by the department to deny ?

If you are sure that policy for appointment is there, you can explore the option and move to High Court.

Consult and engage a local prudent lawyer for appreciation of facts / documents, professional advise and necessary proceeding.

This is a repeat of the same question in different words.

Yes, you can. However, if there is Administrative Tribunal, the Tribunal need to be approached.

You stated that you applied for the post of SI of police post, which is coming under the state government  and not under central government.

Whereas the information provided by you statuing that the central government passed an order to a department that the sports which you represented is coming the central government list of games, but it may not be necessary that this sports/discipline should find a place in the list of of games of state list to offer n employment under sports quota and there is no compulsion on the state government to include this game in the state list also. 

So the sports you represented may not find a place in the state list, therefore in that case even if you file a writ petition before high court, the department concerned may file an objection to your claim and seek to reject your petition on the same grounds.

Therefore you may first ascertain the facts and then plan to move legally, only if it is opined by an experienced lawyer based on the background facts.