In order to keep our cat off the kitchen counter and dining table I made a couple of interior doors which let the air move through the house, but keep the critter in check.
So I inset the screen by cutting a channel. Used 3 inch wood screws counterbored to depth to join the corners. Made a jig to mark the screw hole locations.
The tricky bit was where the doorknob goes and how to transition. I did not have a dado blade, so I made do with repeated cuts instead. I just marked the boards and put a mark on the table saw for where to stop, then adjusted the fence in between cuts.
The screw plugs were painted on a strip of packing tape to hold them still.
Very happy with the results.