Hello Aspirant

Yes,you can easily get admission in government medical college in uttar pradesh with a score of 589 marks and 10471 rank under obc category and state quota.

You can check the list of medical colleges and last year's cutoff for obc category under state quota in Uttar pradesh with the help of link mentioned below-

https://medicine.careers360.com/articles/neet-cutoff-up
I hope this information proves helpful to you.

All The Best