Hello Atiqua, 

Yes you can definitely apply through the all India quota which reserves 15% seats for students that do not belong to the particular state. Admission is conducted through online counseling on the basis of NEET UG marks. You can get further details here : https://www.google.com/amp/s/medicine.careers360.com/articles/telangana-mbbs-admission/amp

Domicile details are mentioned in the official site itself. Generally you get a a2 domicile if you have studied for more than 10 years in west Bengal. But since you studied 11 and 12 under a different state,  a2 might be easier for you to attain. 

Hope this helps :)