Sharma had filed the petition on August 6, a day after the Centre had abrogated the Jammu and Kashmir's special status.
The advocate in his plea has claimed that the Presidential order on Article 370
was illegal since it was passed without the consent of the Jammu and Kashmir Assembly.
In a separate petition filed on August 10, Bhasin said she is seeking a direction for the Centre and the Jammu and Kashmir administration to immediately relax all restrictions on freedom of movement of journalists and media personnel in Kashmir and some districts of Jammu.
The direction was sought to enable media personnel to practise their profession and exercise their right to report in furtherance of their rights under Articles 14, 19 (1) (a) and 19 (1) (g) and 21 of the Constitution as well as the right to know of the residents of the Kashmir Valley, the petition said.
In the petition, the editor said that since August 4, all connectivity was shutdown leaving Kashmir and some districts in Jammu completely isolated and cut-off from all possible modes of communication and information.
Earlier on Tuesday, the apex court had refused to interfere with the restrictions, including the communication clampdown in Jammu and Kashmir, saying that reasonable time should be given for bringing normalcy in the sensitive situation and posted the matter for hearing after two weeks.
Conference, the main political party of Jammu and Kashmir, has also filed a petition posing legal challenges in the apex court to the changes made in the constitutional status of J&K, contending that these have taken away rights of its citizens without their mandate.
Arguing that the legislation approved by Parliament and the orders issued by the President subsequently were "unconstitutional", the petition prayed for these to be declared as "void and inoperative".
The petition has been filed by Mohammad AKbar Lone and Justice (rtd) Hasnain Masoodi, both Lok Sabha members belonging to the NC.
Lone is a former speaker of the Jammu and Kashmir Assembly and Masoodi a retired judge of the Jammu and Kashmir High Court, who ruled in 2015 that Article 370 was a permanent feature of the Constitution.
Some other individuals have also filed a petition in the Supreme Court
but they are not listed for hearing on Friday.