Cat Dog Door Insert for Sliding Patio Door - Sliding Glass Cat Door with Lockable Weather Proof Panel - Adjustable Height 76.38" to 81.1"

"A picture is worth a thousand words" is apropos here; I have no idea what you're describing. Anyway, they make inserts for sliding doors that allow you to have a cat-flap in the insert; no construction required. This is just one example.