It varies each year obviously. And this year is going to be all the way different for sure since the competition has increased so much due to more number of candidates and paper being easy. 

With a score of 358 the AIR should be around 1,20,000-1,22,000. Expectedly the state rank should be around 4800-4900. (this year it's going to vary, I'm just saying this as per the previous years experience ) 

The closing rank for SC category in third round of counseling for MBBS was 5090 (general merit rank). In the mop up round, the closing rank for govt medical college was 5145.

So, YES there are chances of getting admission to a government medical college with this score.

Stay hopeful.

All the best.

EDIT :- The merit list of UP for respective categories has been published. There are a total of about 381 seats (MBBS) for SC category. Hence the closing rank should be between 425 - 450 (SC merit list). It corresponds to an AIR around 1,50,000-1,60,000.

Therefore the cut-off score should be 340-345.

All the best.

Thanks for reading.