You will need Proforma A1 as Domicile Certificate for Candidates residing in the State of West Bengal continuously for atleast 10 years.  This is given by any Government Authority. They might be:

• District Magistrate, Additional District Magistrate, Deputy Magistrate, Deputy Collector, Block Development Officer
• Superindent of Police, ASP, Sub Divisional Police Officer, DSP
• Commissioner, Additional Commissioner, Joint Commissioner, Deputy Commissioner, ACP
• Judicial Magistrate
• Corporation Area Magistrate
• Assistant Secretary
• Deputy Director

So if you cannot find a BDO, you should try a certificate from any one of the above. A signature from the Joint BDO might not work. Alternatively, you can get the domicile certificate from HoD of your College where you studied your 12th from and then you need Proforma A2. The other documents that are required for Counselling are:

High School Mark sheet

12th or equivalent marks sheet

WBJEE Admit card

WBJEE Score card

Seat Allotment Letter

Receipt of Online Counselling Registration Fee payment

Category Certificate if applicable

Domicile Certificate if applicable

Passport Size Photographs