  Given a graded ample, Hausdorff groupoid $G$, and an involutive field $K$, we
consider the Steinberg algebra $A_K(G)$. We obtain necessary and sufficient
conditions on $G$ under which the annihilator of any graded ideal of $A_K(G)$
is generated by a homogeneous projection. This property is called graded
quasi-Baer $\ast$. We use the Steinberg algebra model to characterize graded
quasi-Baer $\ast$ Leavitt path algebras.
