We've got a "fish fryer" that is essentially a "glorified jet burner". We use it at home, but it's too big to haul along for occasional use. We have a Coleman camp stove that we use for frying fish, just set it up on the picnic table, well away from the trailer and especially not under the awning. Except on very windy days, it does a great job.
DW has one of the new "air fryers" that we use at home, it might be adaptable to RV use, but it's a 1500 watt unit, something that would require the generator or a separate power source (our trailer is 30 amps) so between being "too large to pack away easily" and the power requirements, we'll probably never use it in the RV.
We never EVER fry inside the trailer, between the confined space, the "fish smell" and the complete mess it makes, it's just not worth it. We don't fry inside at home either, BTW.
So far, we're happy with the Coleman camp stove, an old large frying pan and enough peanut oil to do the job. Yup, we also still use brown paper bags to drain the grease (shhhh don't tell anybody)