Tiny amount of cases dropped by associate (4)
I believe the answer is:
iota
'tiny amount' is the definition.
(I've seen this before)
'of cases dropped by associate' is the wordplay.
'of' is an anagram indicator (the answer comes from or 'of' the letters).
'dropped by' indicates named letters should be taken away.
'associate' with 'cases' taken away is 'oiat'.
'oiat' is an anagram of 'IOTA'.
(Other definitions for iota that I've seen before include "Jot, particle" , "letter from abroad" , "Old letter" , "The Greek i (4)" , "Contrivance" .)