Crossword Genius

A little cough one has in the morning (3)

Ross

I believe the answer is:

hem

I'm a little stuck... Click here to teach me more about this clue!

'a little cough one' is the definition.
Although both the answer and definition are singular nouns, I don't understand how one could define the other.

'in the morning' is the wordplay.
'in' says the answer is hidden in the clue.
'HEM' is hidden within 'the morning'.

'has' acts as a link.

Can you help me to learn more?

(Other definitions for hem that I've seen before include "Part of skirt" , "Sewn border" , "try to attract attention" , "Double-backed cloth border" , "It draws attention to" .)

I've seen this clue in the Evening Standard.
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