This topic cropped up somewhere on the forum here a while back, pretty sure that there was 'evidence' of a guy who caught a doggy on the fly and/or another guy who caught a ray on the fly.
Unconventional is the word for it. Doggies and ray are not sight predictors and its beyond me how they managed to catch them on the fly, I can only imagine that maybe a touch of bait or some scent was added to the fly - which defeats the purpose somewhat unless you just want the fight to be on a fly rod(?).
Without adding bait or scent then you'd be a long time trying for one of these species! Pretty crazy tbh.
There are some 'unconventional' (tricky) fish that might be worth trying though of you really want to e.g flounder, dab, halibut, gar, cod, pouting, whiting, gurnard, wrasse, scad, bream... There are people who dedicate some effort to some of these species.
Know people that have caught shark (blues and tope) on fly rod but they added bait to the fly.
happy fly fishing..