Old chien, nouvelle trick! Until now, I’d missed the Heart & Soul episode in which the incomparable Jacques Pepin folded sole fillets before cooking them. Sacre bluefish! I knew to tuck and tie the narrow ends of pork and beef tenderloins before roasting, and to pound chicken breasts, for even cooking. But it never occurred to me to tuck the ends of fish fillets. He explained that the side the skin was on must be on the inside of the folded portion because it shrinks more and would fight the fold otherwise. He starts them cooking in the pan with folded ends down.
The square portions look neat, and more of them can fit in the pan. This should work whether you saute, poach, or bake. I imagine that securing the fold with a toothpick would allow deep-frying as well. I intend to tuck&toothpick the next time I cook chicken breasts, for that matter.
I wonder if the folding technique only needed for skinned fillets.
The technique for skin on fish is to dry it very well - scraping with a knife to start then using paper towel. Scoring the skin with diagonal cuts. Then putting it in a hot pan and holding it flat until it sets.
I assume when skinned you can’t get it really dry but scoring would work.