Dear Md Siam Talukder as useful information for this topic I suggest to your attention this conference paper: Conference Paper Metamaterials on antenna solutions

The gain of a patch antenna will be increased when using metamaterial because in this case, the effective sizes of surface results antenna will be increase.

A resonant antenna is a resonant circuit, a metamaterial is also a resonant circuit. Coupled resonant circuits can have useful properties, like increased bandwidth. Look up coupled resonators, double tuned filters, for instance.

Some of the radiation from a patch, for instance, is from the ground. Metamaterials radiate differently to a conducting ground, and can give increased gain in some directions, by reducing radiation parallel to the ground, for instance, or increasing the radiating aperture.