Hey Aspirant !
370 is not such quite a good score but since you have an OBC Certificate, you will have a chance to be in some of the colleges.
The following list shows the name of the colleges in Karnataka which admitted OBC students whose marks where less than 370 in State Quota :

1. Bidar Institute of Medical Sciences, Bidar : 348
2. Raichur Institute of Medical Sciences, Raichur : 338
3. ESI Post Graduate Institute of Medical Sciences and Research, Bangalore : 346
4. ESIC Medical College, Gulbarga : 355
5. Gulbarga Institute of Medical Sciences, Kalaburagi : 347
6. Gadag Institute of Medical Sciences, Gadag : 343
7. Chamarajanagar Institute of Medical Sciences, Chamarajanagar : 346
8. Karwar Institute of Medical Sciences, Karwar : 352
9. Kodagu Institute of Medical Sciences, Madikeri : 347

Although it's been predicted that the cutoff is going to be on the rise this year, but as we can see, te cutoff for these colleges were quite low and we expect them not to rise much thus giving you opportunity to procure a seat.

Go through the below mentioned link to look at the stats :

https://www.google.com/amp/s/medicine.careers360.com/articles/neet-cutoff-karnataka/amp

Hope this helps.

All the Best !

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