what is correct idiom?

Consider X to be Y
Consider X Y
Consider X as Y

Thanks!

all of them are correct.

the first two have exactly the same meaning; you'd use the first only when the extra words 'to be' are justified, either because they resolve some sort of ambiguity or because there's just A LOT of stuff between 'X' and 'Y'.
examples:
Most Americans consider Beverly Hills, a ritzy suburb to the north of Los Angeles, to be a desirable place to live. <-- possible ambiguity (could mean l.a. is desirable) if you don't include 'to be' here
Most Americans consider Beverly Hills a desirable place to live. <-- no ambiguity, so 'to be' would be unnecessarily wordy

--

'consider as' means 'consider in the capacity of or in the role of'. for instance:
Considered as a work of art, Grant Wood's "American Gothic" is wholly unremarkable; considered as a depiction of everyday 1930's Americana, however, it is a classic piece. <-- i.e., the piece is unremarkable [i]from the standpoint of art, but remarkable from the standpoint of american historical portrayal.