Behaved disgustingly in petty quarrel! (4)
I believe the answer is:
spat
I believe this is a double definition.
'behaved disgustingly' is the first definition.
(spat at someone)
'petty quarrel' is the second definition.
(spat can mean a silly argument)
'in' is the link.
(Other definitions for spat that I've seen before include "Short gaiter or slight quarrel (4)" , "Little quarrel - leg wear" , "Bickering" , "Showed contempt" , "Gestured with contempt" .)