Even a smidgen of evidence (4)
I believe the answer is:
sign
'evidence' is the definition.
(I know that sign is a type of evidence)
'even a smidgen' is the wordplay.
'even' indicates alternate letters (even-numbered letters are used).
The alternating letters of 'smidgen' are 'SIGN'.
'of' acts as a link.
(Other definitions for sign that I've seen before include "Evidence" , "Notice; omen" , "Pointer - indicate agreement in writing" , "Manifestation" , "house" .)