This patch has two orthogonal modes. For a circular patch they would be at the same frequency. The cut-outs increase the inductance for the E horizontal mode so decreases the frequency of this mode. It reduces the capacitance for the E vertical mode so increases its frequency. At the frequency halfway between these resonant frequencies, the two modes will be phase shifted by the same amount but in opposite directions. The feed position is at the 45 degree point on the circle and will excite both modes with equal amplitude but they will have different phase because of the slots. The slot should be deep enough to make the total phase difference between the two modes 90 degrees, so the patch will radiate circular polarization. Moving the feed point to the opposite side of the slot will reverse the direction of circular polarization. There may be papers or a section in a book about perturbations to the shape of circular microstrip patches, but I don't know them. You can use simulation to find the right width and depth for 90 degrees phase difference between the modes, then scale the size of the whole shape to get the centre frequency you want.