I mean after inserting the slot of any shape in conventional patch its resonant behaviour changes due to change in L and C value, how we can design equivalent circuit for such geometry?
There is no possible way to retreive an equivalent circuit through simulation (as far as I know). But I did used this paper to build the general understanding of equivalent circuits for microstrip structures (especially for frequency selective surfaces). I hope it can help,
K. Sarabandi and N. Behdad, “A frequency selective surface with miniaturized elements,” IEEE Trans. Antennas Propag., vol. 55, no. 5, pp. 1239–1245, 2007.