Hello,
All the institutes that take students through exams conducted by the government, like, tseamcet, kcet etc., have reservation. If you are searching for colleges which don't fall under the above mentioned category, there are BITS Hyderabad, Mahindra Ecole Centrale etc., in telangana. When it comes to karnataka, there are colleges like amrita bengaluru, jain university etc.,
These institutes are pretty good, but the fee for such colleges is comparatively high. It is not the no.of seats that matters here. All that matters is if the institute joining is good. The best colleges from the 2 states that don't have any reservation are BITS hyderabad and Amrita bengaluru.
Good Luck!