Crossword Genius

Tiny bit of money person has not got left (3)

Ross

I believe the answer is:

sou

'tiny bit of money' is the definition.
(informal term for any small amount of money)

'person has not got left' is the wordplay.
'person' becomes 'soul' (synonyms).
'has not got' indicates named letters should be taken away.
'left' becomes 'l' (common abbreviation).
'soul' with 'l' removed is 'SOU'.

(Other definitions for sou that I've seen before include "Little money once" , "Paltry sum" , "bit of money" , "Former French coin of low value" , "Very small amount of money" .)

I've seen this clue in The Times.
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