Firstly, please also check whether such appointment has been made purely on ad hoc / temporary basis and whether under the rules it is permissible to make such ad hoc / temporary appointment without any examination.
But, presuming that there is no such rule for ad hoc / temporary appointment also, without any examination, in that case one remedy for you is to challenge such illegal appointment by filing a writ petition of quo warranto in the high court under Article 226 of the Constitution. The writ of quo warranto can be filed to challenge the right of an individual to hold an office under the Government, i.e., a Government post, without having proper qualifications or requisites.
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