  Exact supersymmetry can be maintained on nonanticommutative superspace with a
twisted coproduct on the supergroup.We show that the usual exchange statistics
for the superfields is not compatible with the twisted action of the
superpoincare group and find a statistics which is consistent with the twisted
coproduct and imply interesting phenomena such as mixing of fermions and bosons
under particle exchange.We also show that with the new statistics, the
$S$-matrix becomes completely independent of the deformation parameter.
