A bit sozzled to start with, partway through drink (7)

I believe the answer is:

smidgin

'a bit' is the definition.
(I know that bit can be written as smidgin)

'sozzled to start with partway through drink' is the wordplay.
'to start with' says to take the initial letters.
'partway through' becomes 'mid'.
'drink' becomes 'gin' (gin is an alcoholic drink).
The initial letter of 'sozzled' is 's'.
's'+'mid'+'gin'='SMIDGIN'

I've seen this clue in The Times.

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