Hi ioVideoMaker.

Please provide .3dm file of the "remote controller" object.

I think that your attempt with Project and Extrude was close to succeeding, but rather than Planar, try cutting out a piece of the curved surface, to be joined to the extrusion.
Move this curved bottom extrusion 1 mm, and trim it with the edge of the object.
Join and fillet.

- Brian
(This is a mental usage of MoI.)

The last few steps, Trim, Join, Fillet, may instead be Boolean difference of intact solid controller, with the curved bottom extrusion.

ps I missed the part about the groove being 1/3 mm wide, so the extrusion should be two extrusions, one nested inside the other, and only a narrow rounded rectangle strip be cut from the controller...