Topological superconductors (TSC) such as P_x+iP_y chiral superconductors are predicted to be a hunting ground for Majorana zero modes. Although the experimental realization of such a system is scarce, a potential candidate is the transition metal dichalcogenide (TMDC) superconductor, 4Hb-TaS₂ . Misfit materials, close kin of TMDC, consist of TMDC layers sandwiched with rock salt monochalcogenides layers, namely (RQ)_1+x(TQ₂)_n (R = Pb, Bi, or Rare-Earth, Q = Chalcogene, T = Transition metal, and n = 1, 2) which exhibit an intergrowth structure. Due to the different symmetry of the RQ and TQ₂ layers, a misfit occurs along one crystallographic axis even if the other two directions are commensurate. The well-ordered natural heterostructure, significant charge reconstruction effects, along with strong spin-orbit coupling (soc) can lead to emergent properties distinct from those of individual layers, primarily making these families interesting candidates to explore. Here, we have studied the superconducting ground state of misfit layer material (PbS)_1.13TaS₂, which is an alternative stacking of PbS with TaS_2. This material shows superconductivity below 3.1 K, with a critical field exceeding the Pauli limit in the in-plane direction. The specific heat and upper critical field measurement suggest a two-gap superconductivity in this material. The ARPES data shows spin-polarized bands in the material with soc coupling strength 694 meVÅ. The weak interlayer coupling strength of 0.016 eV shows the highly two-dimensional nature of the electrons.