If you've applied against an advertisement, you are a candidate, not an incumbent! Leaving aside the linguistics for a moment, your case will not be tenable. The recruiter always has a right to reject candidate at any stage of the selection process before appointment if you do not meet the prescribed minimum eligibility criteria. It is a settled law that even issuance of an appointment letter is not appointment and can still be cancelled for fair and reasonable grounds. There cannot be any judicial remedy for that since the recruiter has all the liberty to set eligibility criteria suiting its need. The only case would be if the State as a recruiter relaxes the eligibility arbitrarily in favour of any equally placed candidate as you, thus showing unequal treatment of equals.
No Court will ever stay a selection process merely because you feel the eligibility criteria is unfair or feel 'deprived' of employment. A candidate never has a reasonable expectation to be appointed against an advertised employment and there is, therefore, no cause or occasion for any deprivation. He has, at highest, a reasonable expectation to be considered for an appointment and if, after considering the candidate, the recruiter comes to a decision that the candidate is not suitable by virtue of not fulfilling the prescribed criteria, the recruiter is at a liberty to reject the candidate outright.
You are probably mistaken for cases where candidates otherwise not eligible get selected (by whatever means, mistake or otherwise; something which is called ‘irregular appointment’ rather than ‘illegal appointment’) approach the Court, get an interim order against the appointment to the post where they got erroneously appointed, continue employment pursuant to the interim orders and subsequently seek regularization of such erroneous appointment made in their favour. Never happens; such writ petitions are often dismissed with costs. You appear to have been misled.