The pleas -- one moved by the victim father's seeking death penalty for the heinous act and another by the six convicts challenging their conviction -- were listed for hearing jointly along with the plea of one of the convicts seeking suspension of his sentence.
After hearing the case briefly, the bench led by Justice Rajiv Sharma made it clear that the court would deliver justice.
"If we don't hear it, the case will hang," he observed.
His assertions came when senior advocate R.S. Cheema, appearing for the state of Jammu and Kashmir, told the court that an appeal was yet to be filed by the state and all the issues could be taken up together.
Appearing for one of the accused, another senior advocate J.S. Bedi also sought time to argue the case, citing voluminous records.
Refusing to grant a long date, the bench fixed the next hearing in the case for August 7. Simultaneously, the court issued notice to the accused and the state of Jammu and Kashmir.
The victim's father has sought an enhancement of the life sentence awarded to three of the convicts who were sentenced to life imprisonment by a trial court in Pathankot in Punjab on June 10.
The special court had convicted six of the eight accused in the crime and pronounced a life imprisonment to three -- temple priest and mastermind Sanji Ram, Deepak Khajuria and Parvesh Kumar.
Investigating officer Raj Dutta and Special Police Officer Surinder Kumar were also sentenced to five years in jail for destroying crucial evidence in the case.
Sanji Ram's son Vishal was acquitted due to lack of evidence, but the fate of his minor nephew, also among the accused, will be decided by a juvenile court.
According to the chargesheet, the girl, who belonged to a Muslim nomadic tribe, was kidnapped and held captive at a village temple in Kathua district on January 10, 2018.
The 15-page chargesheet said the eight-year-old girl was starved, sedated and repeatedly raped in captivity over several days before being bludgeoned to death.
Her mutilated body was found in a forest on January 17. Three days later, one of the accused -- reportedly a juvenile -- was arrested by the police, the chargesheet said.
The abduction, rape and killing of the child was part of a carefully planned strategy to remove the minority nomadic community from the area, it added.
The case sparked outrage across the state, forcing the government to hand over the case to the Crime Branch of Jammu and Kashmir Police.
The case strained relations between the then ruling coalition partners in the state, the PDP and the BJP, after two ministers of the latter - Chowdhury Lal Singh and Chander Prakash Ganga - participated in a rally organised by the Hindu Ekta Manch in support of the arrested accused.
The Supreme Court later ordered that the case be shifted out of Jammu and Kashmir and be heard on a daily basis by the trial court in Pathankot.