How to reduce/shift the resonant frequency of patch antenna array?

I have designed 2x2 and 2x4 circular patch antenna arrays operating at 2.4GHz. To further improve antenna performance(gain) i have introduced air gap layer between substrate and ground plane. But that has shifted the resonant frequency towards right (between 3GHz to 3.5GHz). How do i reduce or bring back the resonant frequency to 2.4GHz without changing Patch dimensions, effective permittivity or substrate height?

You have forbidden us to use any of the knobs that could do what you want. What did your simulation say before you built the arrays?

here is the Consolidated Return Loss report for different air-gap heights (A)

This is expected, because you have lowered the effective permittivity of the substrate (mixture of er=1 and PCB).
You need to compensate that by larger patch dimensions, or higher PCB permittivity.

Yes but once an antenna is fabricated Patch dimensions, permittivity, substrate height cannot be changed. So i need external controlling factor for tuning frequency of antenna. Looking for other options like slots, DGS, diode etc not sure which one would help.