Crossword Genius

Bird inside of skip found by waif, oddly (4)

Ross

I believe the answer is:

kiwi

'bird' is the definition.
(kiwi is a kind of bird)

'inside of skip found by waif oddly' is the wordplay.
'inside of' indicates the central letters.
'found by' is a charade indicator (letters next to each other).
'oddly' indicates alternate letters.
The middle of 'skip' is 'ki'.
The alternating letters of 'waif' are 'wi'.
'ki'+'wi'='KIWI'

(Other definitions for kiwi that I've seen before include "New Zealander's bird" , "N Zealand bird" , "apteryx" , "Someone from Auckland?" , "Hairy fruit with green flesh" .)

I've seen this clue in The Times.
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