Telerik.Cms.Engine.WebControls.GenericContent is a custom control which does not inherit from UserControl class. Also, if you are using UserControls, you cannot inherit other controls, since User Controls must explicitly inherit from System.Web.UI.UserControl class and in C# it is not possible to inherit from more than one class.
Therefore, if you are trying to extend GenericContent control the best way would be to create a new Class Library Project, create there a new class and inherit from GenericContent. Obviously, you will not have the benefits of using the visual drag-and-drop interface, but there are ways to work around this through use of templates.
You can refer to this article in the Developer Manual which explains how to extend ContentView control:
Even though they are different controls, the principle is exactly the same and I believe it would be very helpful to you in your endeavor to extend GenericContent control.
I hope you will find this information helpful. Let us know if there is anything else we can do for you.
the Telerik team
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