Hello aspirant,

As you belong to the ST category with a score of 444 you have good chance of getting a seat in government college. You haven't mentioned your state. You can get a seat in government college in your state as there is 85% reservation for state candidates. you can also get a seat in some states through All India Quota like in Karnataka. So you have good chances of getting a government college seat. So you can try sccordingly. If you want to predict the colleges which you can get with this score use the link provided.

Http://www.medicine.careers360.com/neet-college-predictor

Hope this helps
Thank you.