Yadav had sought early hearing on the ground that his mother was unwell but Justice Indermeet Kaur declined the relief and said the matter would be taken up on the date already fixed on April 10.
The plea was opposed by the state, represented by Additional Criminal Standing counsel Rajesh Mahajan, saying no medical records of his mother have been placed on record to show there was any urgency.
The court had earlier asked why the relief be not granted to him if there was no apprehension of a threat to the witnesses, including the victim's mother, in the case.
However, the victim's mother, Neelam Katara, and another witness, Ajay Katara, strongly opposed grant of furlough to the convict.
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The police has also opposed grant of furlough to Yadav on the ground that he did not satisfy the eligibility requirements for the relief.
On August 29, 2017, the Supreme Court had dismissed his plea seeking review of its verdict sending him to prison for 25 years.
The apex court had also awarded a 25-year jail term to his cousin Vishal Yadav and 20 years in prison for third convict Sukhdev Pehalwan in the case.
The top court had earlier dismissed the appeals against their conviction in the case of kidnapping of Katara from a marriage party on the intervening night of February 16-17, 2002 before killing him for his alleged affair with Vikas Yadav's sister Bharti.
Katara was murdered as Vishal and Vikas Yadav did not approve of the victim's affair with Bharti because they belonged to different castes, the lower court had said in its verdict.