Godot doesn't support exporting arbitrary types, it has to be a primitive type or a
Resource (which can be a custom one).
I haven't done that often and I don't use C# in Godot, but here are some suggestions:
If you want to export your custom type you could make it inherit
Resource and export it as
Then in the inspector, under the property, create a new
Resource, and add your custom resource script on it. At least, that's how it can work in GDScript.
If that doesn't work, try to make your field a
Resource instead of
MyClass, then cast it to obtain your derived type.
You could bypass the extra step of adding resource + adding script by registering your class with a global class name so it will appear in the
New Resource dialog (a Godot feature, not related to C#) but I haven't tried with C#.