A bench of justices S A Bobde and L Nageswara Rao said Acting Chief Justice D N Patel may appoint an independent officer to look into the alleged irregularities, noting it was a "serious matter" which could "bring the administration of justice into disrepute".
The top court asked Justice Patel to get an enquiry done into the circumstances under which the contradictory orders were passed, how they got uploaded in the high court website and later removed.
The apex court's direction came on a plea of Congress legislator from Barkagaon in Jharkhand Nirmala Devi against the rejection of bail order by the high court in a case related to violence in the constituency.
The bench noted that orders passed by the high court in the two bail applications of Nirmala Devi and Yogendera Sao were in two parts each.
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It said that in the case of Nirmala Devi the parts of the order had similar reasons and concluded that her bail plea be rejected.
However, in the second part, the judge had given reasons for grant of bail, the top court said.
Senior advocate Vivek Tankha, appearing for Nirmala Devi, said that the second part of both the orders were initially uploaded on the website of the high court but subsequently removed and were not there on the website.
"We consider this to be a serious matter and having a tendency to bring the administration of justice into disrepute," the apex court said.
Both Nirmala Devi and Sao were accused in the case pertaining to violent clashes between villagers and police in 2016 in which four persons were killed.
Nirmala Devi had led the agitation against National Thermal Power Corporation authorities for their alleged attempt to forcefully evacuate villagers from Barkagaon without giving them due compensation or rehabilitation.