If you have applied for probate you don’t need succession certificate 

probate would be granted fir all her immovable and movable assets 

inform  entities that you have applied for probate of sister will 

A succession/legal heir certificate  is issued by the  office of Tahasildar to the legal heir of deceased. It is issued for obtaining pension benefits of deceased Government employee or appointment on compassion ground. It is also used to claim insurance, share certificates, access to bank deposits of deceased account holder. Submit the application form available in the  office of Tahasildar affixing 2 rupee court fee, with death certificate, aadhar card of applicant, names of other legal heirs.

1. You'll have to move the civil court having jurisdiction for the Succession Certificate. 
2. I extend my services as a counsel for moving such a petition. However, I require a consultation session with you first. You have to visit me for it. I'm based in Mumbai /NaviMumbai and hence you should have no issues visiting me as I understand you too are in Mumbai. 
3. ९८२०८९७८८४. (nine eight two zero eight nine seven eight eight four) 

If there is a clear description of all the assets both movable and immovable left behind by her duly bequeathed them in her Will, then the probate of Will would be more than sufficient for claiming all her dues available with any entity.

If there is no specific mention about all the assets or if some of them have been missed out in the Will then she may have to file a suit for declaration to declare her as the surviving legal heir to succeed to all the estates of the deceased person in the capacity of biological mother to the deceased daughter. 

Since your mother is not falling under the list of class I lgal heirs, the Tehsildar cannot issue a legal heirship certificate to your mother because of this.

The Tahsildar is empowered to issue legal heirship certificate only in respect of class I legal heirs.

The list of legal heirs as per Hindu Succession Act  is given below:

15. General rules of succession in the case of female Hindus.—

Dear client,  For a succession certificate, one should need to apply to a magistrate or a high court. Usually, courts have a separate cell that issues succession certificates. When it comes to immovable property , there are other documents, like, for instance, a gift deed, that can help.

As the Will is already under he process of being probated, there is absolutely no need for any succession certificate for the assets covered under the Will.

i dont think you need to get a separate succession certificate

the Will makes a bequest for 'all her assets and funds'

so the executor of the Will can very well administer such assets and funds as well and any bank or MF house should have no problem releasing the funds to such an executor, after the Will is probated

You need to apply it to HC or appropriate court depending on jurisdiction of property. Court will issue you the sane