my expected neet 2020 score is 586. I am from general category in uttar Pradesh. Is there any chance of getting the government college.

586 is really a very good score. You know that the cutoffs change every year so it is quite difficult to predict. Now going by last year cutoffs you have fair chances at Government Medical College, Sahranpur; Government Medical College, Azamgarh; Government Medical college Badaun; Government Medical College Kannauj and Ambedkarnagar. You can check the cutoffs here http://medicine.careers360.com/articles/neet-cutoff-up But these are based on previous year data and this year it might change. So I would suggest you to use our neet college Predictor tool to know where you have good chances http://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer