Hi,
In all lights, you have an option to check or uncheck Cast Shadows option,
But if you like to do it on an object basis, just select the object, right-click, Object Properties,
There you can uncheck the option: Cast Shadows.
If you're talking about those encircled in red, I think these are reflections and not shadows
If that's the case you need to turn off the reflection of that material, or, also in the Object Properties
Mentioned in my previous reply, you can uncheck the option "Visible to Reflection/Refraction"
You didn't mention what rendering engine you're using, and the type of materials, lights, etc,...
But anyway check the reflectivity thing in the material editor or in the Object Properties.
I created a simple test scene with surface materials, Arnold light,
Check the parameters encircled in red
Notice that Metalness is 0
Oops! I didn't notice your reply! :))
I had this window opened for a while, I got busy, then I posted it! 😄
Anyway glad it worked!