Mahendra, you haven't mentioned your Category. This is important because every Category has different cut offs. With a score of 620, your rank might be approximately between 4074-5630 . This is an expected rank range: https://medicine.careers360.com/articles/neet-result-marks-vs-rank . Now regarding the Colleges that you may have a shot at, you have a chance in:

• MP Shah Medical College
• Goa Medica College
• GSVM Medical College
• Gajara Raja Medical College
• Gandhi Medical College, Bhopal

Having said that, this is based on 2019 data and cut offs change every year. Cut offs change every year depending on various factors such as no.of Candidates appearing for the exam, no.of Candidates qualified, top NEET score and difficulty of the exam. For a complete list of colleges that you may have a shot at, please use our College predictor: https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer

Dear student
At first congratulations and best wishes for your result . You have not mentioned your category so I am assuming you as an general category candidate. I am happy to say with this marks your chances to get government colleges are very positive through All India counselling for 15% seats. Some top most best government colleges that you can get are

Darbhanga Medical College, Laheriasarai

Guwahati Medical College, Guwahati

Nalanda Medical College, Patna

Goa Medical College, Panaji

Indira Gandhi Institute of Medical Sciences, Patna

Pt. D.D.U Medical College, Rajkot

Kalpana Chawla Govt. Medical College, Karnal

M.P. Shah Medical College, Jamnagar

Rajendra Institute of Medical Sciences, Ranchi

Mysore Medical and Research Institute, Mysore

Dr. Rajendra Prasad Medical College, Tanda

Government Medical College, Kottayam

Gandhi Medical College, Bhopal

Government Medical College, Thrissur

Government Medical College, Amritsar

R.N.T. Medical College, Udaipur

Government Medical College, Nagpur

Moti Lal Nehru Medical College, Allahabad

Stanley Medical College, Chennai

Etc.

You can try in state counselling for remaining 85% seats also. Different state counselling cut offs vary from each other.
For different states it depend upon availability of colleges, student number etc various things . You have not mentioned your state . You must mention that for us to answer precisely. You must go for your respective state's counselling. Even there chances for you are easy for government colleges. Also you can get easily many private medical colleges.
You can further check on our link
https://medicine.careers360.com/articles/neet-cut-off-for-government-colleges
predict your chances here
https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer
Best Wishes.