I am looking for a solution to find the percentage area covered by a polygon inside another polygon, from geo coordinates using python. 
The polygon can be either fully reside inside the other one or a portion of the second polygon.
Is there a solution to this. 
Please advice.
Percentage is just area of intersection over area of the (other) polygon:
area(intersection)/area(polygon2).
Basically any of geometry packages should be able to compute this, as they all support area and intersection functions: I think Geopandas, SymPy, Shapely (and others I missed) should be able to do this. There might be differences in supported formats. 
You did not specify what Geo coordinates you use though. I think Geopandas and SymPy support only 2D maps (flat map) - meaning you need to use appropriate projection to get exact result, and Shapely works with spherical Earth model.
Python package/function to get percentage area covered by one polygon in another polygon using geo coordinates