In a world where communication requires ever faster data transmission capable of transmitting high speeds. In order to reach and transmit this high speed, it is necessary to increase the frequency that carries the information. For this, scientists are interested in the terahertz (THz) range which, thanks to its high frequencies between 0.1 THz and 30 THz, offers the possibility of increasing the data rate. This letter presents the inclusion of Dodecagon Split Ring Resonator (D-SRR) in rectangular microstrip patch antenna and its effect in the performance of the proposed antenna. The metamaterial design employs two types of SRRs resonators shapes such as the Dodecagon Broadside Coupled Split Ring Resonator (DBC-SRR) and Dodecagon Split Ring Resonator (D-SRR). The model applied uses a local field approach and allowed to obtain the dispersion characteristics of discrete negative magnetic permeability. The proposed antenna substrate uses Arlon AD1000 material, which helps to attain high gain and good directivity at THz frequency. The antenna performance is investigated with and without superstrate. The operating frequencies of the proposed antenna vary in the range of 0.66 - 0.69 THz and shows maximum gain of 10.4 dB and maximum directivity of 9.84 dB. HFSS software tool helps to simulate the parametric analysis of the proposed antenna design. This novel structure may find applications in terahertz imaging, remote systems and may find manifold possibilities in the medical field.