You have to file a petition in the District Court, making all the legal heirs as petitioners and ALL CONCERNED & PUBLIC IN LARGE as the respondent along with all required documents including death certificate of your father. You have to pay 5 to 6 % court fees on the value of the share certificate into the court. The court will publish a PUBLIC NOTICE in two local newspapers calling for objections from any interested parties. After one month, if there are no claims from anybody, it will grand succession certificate in favour of the legal heirs.
Since your father is died, You, your sister and your mother can claim equal rights in share certificate. If you want to transfer the share certificate only in the name of your mother, you and your sister should give NO OBJECTION to the DEMAT account staff. There will be a form specially meant for it.