Possible representative of market-goer at home periodically (3)
I believe the answer is:
toe
'possible representative of market-goer' is the definition.
(ref to nursery rhyme This Little Piggy)
'at home periodically' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'at'+'home'='athome'
The alternate letters of 'athome' are 'TOE'.
(Other definitions for toe that I've seen before include "Small member" , "'Little piggy'" , "Calabria?" , "Lower tip of something" , "One of the lower digits" .)