Article 35A of the Constitution defines "permanent residents" of the state and bars non-residents of Jammu and Kashmir from buying immovable property under state subject law. It also confers special rights and privileges in jobs and acquiring property to permanent resident of the state.
Petitions say the provision is against the spirit of oneness of India and discriminates against citizens from other states. A petition also says the article discriminates against women of the state, who lose their right to own property in the state if they marry a "non-resident".
Chief Minister Mehbooba Mufti has said that if it is tinkered with, then it will have a direct impact on demography of the state.
The centre has told the court that the question is "very sensitive" and requires a "larger debate".
Ms Mufti was reportedly told by the centre that in the Supreme Court, it will present the legal aspects as they exist in the Constitution.