You're a floozy meatarian if all you have tasted is chicken and mutton. But if the dearth of shops selling unconventional meat is what you are complaining about then hit up one of the government Haringhata Stores that now dot across the city.
The Haringhata Stores are part of the West Bengal Government Livestock Development Corporation Ltd. These shops now spread across the expanse of the city (Camac Street to Jadavpur, Baguihati and Behala) stocks up on meat and diary products that comes from the livestock farms that are monitored by the government.
Locally reared and under the supervision of the government, these Haringhata shops sells frozen processed meat and cold cuts. From the usual chicken and mutton pieces to your sausages and seekh kebabs - they stock all sorts here. Even unconventional meat that are not so easily available in the market, like that of quail, turkey, rooster, rabbit, duck and emu is also available here. In fact, you can also grab some pork, free range chicken and eggs at these stores.