you should apply to housing society to delete mother name in share certificate 

enclose mother  death certificate , legal heir certificate 

latest receipt of payment of society maintenance dues

As the property was registered in the names of your father, your mother and you, each of you have one-third undivided share in it. After the death of your mother, her one-third undivided share devolved on her legal heirs equally, namely, your father, your sister and you. As of now, your father, you and your sister's undivided share will be 44.44%, 44.44% and 11.12% respectively. Now if you wish to sell the property, all the three of you will have to sign and register the sale deed. Or, if your sister and father forgo their respective undivided shares in your favour by executing a deed of relinquishment, you alone can sell the property.

You call can execute the sale agreement with the seller and sell the flat. As your mothers share devolve to you. If she has any will then no need of letter of administration from court. Otherwise court order will be required in form of letter of administration. But if buyer is ready with the same you can execute an indemnity bond to him to avoid letter of administration 

Your mother's share will devolve equally on all legal heirs namely your father,  sister and you 

You and your father are entitled to 1/3ed share each besides  all the three of you are entitled to 1/3 ed share out of your deceased mother's share of 1/3rd in the property.

As your mother is reported to have died intestate the revenue records in respect of her share should be transferred to all your three names.

After that all the three of you can sell the property by jointly executing the registered sale deed in favor of the prospective buyer. 

- As per law, after the demise of your mother intestate , his share in the said property would be devolved upon all her children equally. 

- Hence, if you are three are only surviving legal heirs then you three will get equal share in her 1/3rd share 

- If you three are agreed for selling the same then you can apply for mutation of the said property in your names first then sell the same

Please apply for a succession certificate from court. 

Dear Client, kindly note the following points,

On getting the legal heir certificate, get mutation of the property done in the local municipal records to remove your mother's name and insert names of the heirs accordingly. All co-owners (your father, you, and your sister if she gets your mother's share) have to give consent to sell the property. The sale of the property is not possible without everyone's consent in the said case. Get the property valued by a registered valuer to arrive at the market price (approximately ₹45-50 lakhs as per your previously states estimate). You are directed to consult a lawyer and draft a sale agreement executed by all co-owners and the buyer, indicating terms of sale and proportion of proceeds. Register the sale deed before the local sub-registrar office with signatures by all co-owners. Transfer the sale proceeds among co-owners proportionate to their respective shareholdings. It is better to hire a lawyer to manage the legal technicalities, particularly succession transfer and registration of sale deed.

Dear Sir/Madam,

It is not clear from your query that whether the name of your sister also inclduded in the share certificate of the flat after demise of your mother. Leave aside this, fact, it is suggested that in the present circumstances, there will be 03 sellers in the present circumstance, you, father and sister. Get the sale deed well drafted including all the facts i.e. the facts of registration, demise of mother, family tree and present heirs of mother with their share and their intention of sell. This will make the sell error free.