Glass reflection distortion Which factors should I look at to make the reflection as neat as that of the reference image?
Some of the thigs I've tried:

Increasing roughness, but still have too many distorted reflections and also I can't see the yellow sphere in the cube clearly like the reference image.

Changing variables on Ray visibility, but nothing seemed to work. Material of the cube is set to default material with : Specular 0.5 / Roughness 0 / Transmission 1 level


Reference

My Cube  – Bottom and left sides has way too many distortions.
Those things at the bottom are reflections (as you mentioned) so care about environment you use.
For distortion you can try to play with IOR value.
Another thing to care is curvature of your Cube - more rounded more distortions.
Here White environment with a bit of Beveled edges and IOR 1.15