Hi there. 

To avail seats under the 85% state quota the candidate needs to prove that he is a domicile of that particular state which requires a domicile certificate. 

If you have a domicile certificate of the state of Karnataka then you'll be eligible for the 85% state quota counselling of Karnataka's state. 

Moreover, Hyderabad is only a city. And, in NEET, admission occurs on the basis of 15% all India Quota and 85% state quota. City quota's do not exist. 

Logically, if your Aadhar mentions Karnataka you will eligible to avail seats under Karnataka's state quota. 

Wishing you luck!