This type of caustics is exactly where one would use a pathtracer. Eevee doesn’t support it.
This is closest way to fake what you’re asking and I don’t really see a way to add color to it. If you really need to have similar effect in Eevee then consider baking it in Cycles and adding it to appropriate materials or faking it with subtle spotlights or similar techniques.
Edit:
One similar solution, but If you don’t use it just as a shadow catcher you’re going to have to compromise on the quality of the original material that would recieve the colored shadow: How to colorize Eevee shadows? - #4 by filibis
Might be a way to get more flexibility with it and duplicate the geometry that would catch the shadow and have it as a “overlay” over the original geometry with the non shadow part completly transparent and shadow with some opacity.
Edit 2:
Like this. Woudn’t consider it practical though.