Hi Anshu,
Please be duly informed that the candidature of both a private candidate and a candidate who appeared the examination through some school is exactly same in terms of hierarchy of academic standard and thus it would not make any difference in future prospects. The only aspect that is different as a private candidate is that the candidate does not appears the examination through any school and prepares by oneself for the examination an there is no harm in that. The only thing that matters for your future endeavors is your academic excellence and nothing else.
And as for government jobs and competitive examinations the only academic criteria they have for suitable eligibility is to have passed class 10 or class 12 or higher education for that matter and a certain cut off percentage in the same. So rest assured that your private candidature won't bar you from these applications.
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