  We study the relations between the quaternion $H$-type group and the boundary
of the unit ball on two dimensional quaternionic space. The orthogonal
projection of the space of square integrable functions defined on quaternion
$H$-type group into its subspace of boundary values of $q$-holomorphic
functions is consider. The precise form of Cauchy-Szego kernel and the
orthogonal projection operator is obtained. The fundamental solution for the
operator $\Delta_{\lambda}$ is found.
