  We describe all blocks of the category of finite-dimensional
$\mathfrak{q}(3)$-supermodules by providing their extension quivers. We also
obtain two general results about the representation of $\mathfrak{q}(n)$: we
show that the Ext quiver of the standard block of $\mathfrak{q}(n)$ is obtained
from the principal block of $\mathfrak{q}(n-1)$ by identifying certain vertices
of the quiver and prove a ''virtual'' BGG-reciprocity for $\mathfrak{q}(n)$.
The latter result is used to compute the radical filtrations of
$\mathfrak{q}(3)$ projective covers.
