In my opinion, you have the following options:

1) Appeal to the courts, perhaps civil court - I think this matters comes under the domain of utter disregard for fundamental rights. They could disqualify you after the interviews but to challenge the elagibility is I think in principle very wrong.

2) Goto the MNA or MPA - Perhaps the proper channel of voicing your concerns on a national level is this one. However, the availability and readiness of the member cannot be guaranteed.

3) Goto the educational department (civil service) - The Education ministry may exercise some influence on these institutions but I dont think without any personal interest of some higher-up, you'd really be able to avoid the hectic red tape procedures.

4) Goto the media - Pakistani media has their own interests and unless some media person has a personal grudge with the management of institute, they would not really be keen to help.

Now I am not trying to be cynic here but theres a high probability of the above scenarios happening to you. But dont lose hope, this is precisely the reason why we want to join the civil services, not to change system but to change people, to provide environment conducive to the growth of honesty and justice in the society.

And dont let this incident kill your motivation and remember,
"that dont kill me can only make me STRONGER"

I shall pray for all those who have been a victim of such crude injustice.

All the Best~

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Love me or hate me, both are in my favor…If you love me, I'll always be in your heart…If you hate me, I'll always be in your mind -- Shakespeare