Correct spelling


Correct spelling, explanation: duly is the correct form, because the base adjective is due and we add adverbial suffix -ly. Duely is incorrect, because we should omit e: duly is an exception of the rule that we don’t drop the e after a vowel. This is because in case of due and true silent e doesn’t determine the pronunciation of any other letter. E is there so the words don’t change with u; thus we omit the e with suffix -ly.

Definition of duly:
adverb, in a proper manner
We only accept originals or duly authenticated copies.
Please duly inform the other party before cancelling the appointment.

Incorrect spelling


Incorrect spelling, explanation: duely is an incorrect form, because due and true are two adjectives which are exception of the rule that e can remain after adding suffix -ly. This is because of the fact, that silent e doesn’t change the pronunciation in any way, so it’s just there for the words not to end with u. Therefore we can drop it with the suffix and we receive duly and truly. This is why duly is the correct form.