Happy and Blessed Ganesh Chaturthi!
Sorry for the delayed response.
You could have a look at Howard Public School, Vasavi Public School in Himayat Nagar and Rishi Public School in Basheerbagh.
You could visit these schools once to check if it suits your child.
Oxford Grammar School in Abids is good and near for you. Apart from these you could consider the below schools which are a bit far ( 10 km radius). They are quite old, leading and established schools.
BVB - Vidyashram on Rd no 61, Jubilee Hills,
BVB- Atmakuri on Rd no 45, Jubilee Hills,
Jubilee Hills Public School,
P Obul Reddy School in Banjara Hills,
Meridian School - Banjara Hills....
You could call up the schools to know admission schedule. All schools have different admission dates, so it is better to follow up from this month onwards.
You could write to me in this thread. I will try to reply soon.