what are the legal rights of a will ?

We are jains.My maternal grandfather died 19 yrs back leaving will(not registered) in which he had gave all the movable and immovable property to my maternal grandmother.my maternal Grandma died dis year leaving a registered will in which she stated 50-50 to my mother and hes sister and not given any share to der 3sister(she died in 1996) as we don't have any relationships wid dem due to personal issues.after my maternal grandma's death my cousins(they r two brothers)son of 3rd sister filed a caveat and letter of administration for his share and stated dat my grandma haven't made any will.but we do have Registered​ will.and already we have started the procedure of probate.So my question is applying for probate is right solution to it?and does he have any right in the property and other assets of my maternal grandma?and if no Dan how much time it would take for the case to settle down.