Three-family supersymmetric Pati-Salam models with symplectic groups from intersecting D6-branes

We construct new three-family $\mathcal{N}=1$ supersymmetric Pati-Salam models from intersecting D6-branes with original gauge group $\mathrm{U}(4{)}_C\times \mathrm{U}\mathrm{S}\mathrm{p}(2{)}_L\times \mathrm{U}(2{)}_R$ on a Type IIA ${\mathbb{T}}^6\mathrm{/}({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ orientifold. We find that replacing a $\mathrm{U}(2)$ with a $\mathrm{U}\mathrm{S}\mathrm{p}(2)$ group severely restricts the number of three-generation supersymmetric models such that there are only five inequivalent models. Exchanging the left and right sectors, we obtain five dual models with gauge group $\mathrm{U}(4{)}_C\times \mathrm{U}(2{)}_L\times \mathrm{U}\mathrm{S}\mathrm{p}(2{)}_R$. These ten models have different gauge coupling relations at string scale. The highest wrapping number is 4, and one of the models contains no filler O6-planes. Moreover, we discuss in detail the particle spectra, the composite particles through strong coupling dynamics, and the exotic particle decouplings. Also, we study how to realize the string-scale gauge coupling relations in some models.