Bill's child (4)
I believe the answer is:
chit
I believe this clue is a double definition.
'bill's' is the first definition.
(chit is a kind of bill)
'child' is the second definition.
(thesaurus)
(Other definitions for chit that I've seen before include "Impudent youngster" , "Pert young lady" , "Tab" , "bill to pay" , "Impudent girl" .)