You cannot do it with AutoCAD .NET API. It can be done with quite involved effort and I would rather use .NET API's PaletteSet to display custom data in most cases.
There have been a few discussion on this topic, such as this:
https://forums.autodesk.com/t5/net/autocad-s-properties-palette-modification/m-p/12341073#M79279
You might want to read this post. They claim to have accomplished it based on this article.
Ed
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