Plot polar coordinates (2D) on a Poincáre Sphere surface as either heat map or scatter plot

I have a dataset with 4 values - amplitude, psi angle, chi angle and class (color).

The psi angle and chi angle represent unique points on a .

I want plot these psi and chi values on this sphere co-ordinate system as a scatter plot.

After that, I'd like to use the amplitude value as the histogram coming out of the sphere at certain height.

Each class can be represented by a color.

I was trying something in python matplotlib but couldn't find anything which would do this. How can I plot such a scatter histogram plot on spherical co-ordinate system.