Halfwit forgetting ID, a Greek character (4)
I believe the answer is:
iota
'greek character' is the definition.
(letter from the Greek alphabet)
'halfwit forgetting id a' is the wordplay.
'halfwit' becomes 'idiot' (I've seen this before).
'forgetting' indicates named letters should be taken away.
'idiot' with 'id' taken away is 'iot'.
'iot'+'a'='IOTA'
(Other definitions for iota that I've seen before include "very small part" , "(Not one) little bit" , "Greek letter - small quantity" , "Ninth letter of Greek alphabet, small amount" , "Smidgen" .)