A novel kind of microstrip patch antenna is proposed in this paper. The antenna layout consists of a probe-fed circular patch integrated on a grounded slab of inhomogeneous artificial dielectric. A rigorous full wave analysis of this radiation component is here developed starting from the determination of new expressions for the spectral dyadic Green's function that take into account the inhomogeneity presence. The spectral Green's dyad is also obtained in the Hankel domain and a complete and accurate Method of Moments (MoM) is presented. Finally, several numerical results, obtained by means of a self produced code based on the theory here developed are presented in order to show the main capabilities of the novel antenna. Particularly, the comparison between the radiation pattern and the input impedance of such an antenna and those obtained for a similar one with a homogeneous substrate shows an improvement of both the directivity and bandwidth.