With 350 marks in neat general category, you are in the 70,000 to 1,00,000 at range. This makes you eligible for a seat in several government, BDS colleges by states and cut-offs.
Government BDS colleges, you can aim for

SCB dental College and Hospital, Cuttack
Burdwan Dental College, Kolkata
Dr Ahmed dental College Kolkata
GDC Ahmedabad
GDC Jamnagar
Government dental College, Kerala

And with 350 marks in NEET, the following are the possible dental colleges:

Private Dental Colleges

- Manipal College of Dental Sciences: inr22,10,000 (total fees)

- Sri Ramachandra Dental College: inr6,00,000 (1st year fees)

- Saveetha Dental College: inr9,10,000 (1st year fees)

- A B Shetty Memorial Institute of Dental Sciences: inr5,13,500 (1st year fees)

- Bapuji Dental College: inr4,80,290 (1st year fees)

Government Dental Colleges (Possibly Higher Marks Required)

- Maulana Azad Institute of Dental Sciences: Highly competitive

- Government Dental College, Bangalore: inr2,50,500 (1st year fees)

- Nair Hospital Dental College: inr1,03,900 (1st year fees)

Visit the website of every college to get the updated cutoff ranks and other admission information