## 1 Introduction
The fractal Sierpinski-shaped antenna concept helps to target multiple wireless applications with miniaturization features [27]. A superstrate provides an effective way to reduce the mutual coupling between radiating elements. It reduces the turns' mutual coupling and supports the antenna's directivity improvement [28; 29]. There are many methods available for the antenna's improvement, such as an array of the antenna, a surface-mounted horn antenna, composite conductors and a lens antenna [30; 31; 32]. At the same time, the main limitations of these designs are the large space requirements and the hardware needed for the high-gain antennas [6; 33]. The listed problems are solved by adding artificial properties to the material, these are called metamaterials. Metamaterial provides a negative value of permittivity (\(\mathsf{\Xi}\)) and permeability (\(\mathsf{\mu}\)) [34]. The primary elements for making metamaterial are the complementary split-ring resonators (CSRRs) and metal wires. The gap between the two terminals of a metal wire behaves as the capacitance, and their curvature shape provides an inductance effect. The size of such a structure is less than the ordinary resonating structure [35]. The metamaterial approach helps to achieve targets, due to their negative permittivity and negative permeability concept [36]. Metamaterial-based designs are used for making perfect lenses, invisibility cloaks, electromagnetic bandgaps (EBGs) and photonic bandgaps (PBGs) [37]. In antenna development, the composite electromagnetic bandgap structure (EBG) and the metamaterial inhibit the electromagnetic wave for a specific range of frequency [38; 39]. This structure innovates a new way of developing compact and better performing RF components [40]. The two-dimensional EBG design confines the surface wave in a patch structure and metamaterial, enhancing the antenna's gain, directivity and reflectance response [41]. There are a few possible ways for the miniaturization of metamaterial antennas. First is a substrate with a high permittivity, a low tangent loss and a rising thickness. Second is a zero-impedance plane, similar to the perfect electric conductor. Third is inserting an infinite impedance identical to an excellent magnetic conductor. Efficiency, in the third case, is reduced due to the dissipative loss [42; 43]. Fourth is using metamaterial above a patch antenna to condense the surface waves. An array of metamaterial rings will enrich the antenna's gain, but it also increases the size of the antenna. The solution is provided by inserting a tooth on the exterior surface of the ring [44]. The manuscript presented here represents a novel metamaterial-based multi-layered superstrate structure, to achieve the multiband operation for S, C and X frequency bands. Gain improvement has been achieved by adding a tooth to the metamaterial structure [45]. Four designs are simulated to achieve a high gain, multiband and broadband characteristics. The first design is a patch with connectors and metamaterial rings with the tooth. The second is a patch with connectors and metamaterial without a tooth. The third is a patch without connectors and metamaterial with the tooth. Fourth is a patch without connectors and metamaterial without a tooth. The charge distribution in the patch region is affected, due to the connector section of the exterior and interior patch elements. Therefore, it leads to a change in the reflectance response plot. The effect of the tooth over the metamaterial loaded structure helps to attain a better performance. All designs are compared using different substrate materials, such as Rogers RT Duroid 5880 and FR4 materials. The simulated results are compared, in terms of the number of bands, the bandwidth, VSWR, the reflectance response (\(S_{11}\)) and gain.