Does anybody know the exact issue when Illyana was first shown as Darkchylde? I can't find it anywhere.

Issue #4 of Magik limited series from the 80's

Bringing back and old topic, but my question is mainly connected to this particular spelling. Was Illyana ever truly call "Darkcylde" with the "y" in comics, or is it misspell by fans?

It's had various spellings.  Usually with or without an 'e' on the end.  I don't remember it with a Y from the original New Mutants series (which I recently re-read), but I might have just missed it just out of habit.  The spelling, puntuation or grammar of fans isn't the best.  So I wouldn't be surprised if it was a recurring typo (like Rouge instead of Rogue, or Ice Man instead of Iceman).  Or maybe some fans are confusing her for Darkchylde.

Yeah I'm shifting through the New Mutants myself at the moment, and didn't see it spelt with Y, hence the question.