No, there isn't a chance for getting admission into Osmania University's MA in Economics program without appearing for an entrance exam.
As of July 1, 2024, Osmania University requires an entrance exam score for admission to its MA programs, including Economics.

The university conducts its own entrance exam called the Osmania University Common Entrance Test (OUCET), but it has recently been replaced by the Common Post Graduation Entrance Test (CPGET).

Admission to MA Economics is based on the rank or merit secured in the CPGET exam.

If you are interested in pursuing MA Economics at Osmania University, focus on preparing for the CPGET exam. You can find resources and study materials online or through coaching institutes.

https://www.careers360.com/university/osmania-university-hyderabad

I hope it helps!