The ground-state topological properties of ultracold atoms in composite scalar-Raman optical lattices are systematically investigated by solving the two-component Gross-Pitaevskii equation through the imaginary time evolution method. Our study focuses on the interplay between scalar and Raman optical lattice potentials and the role of interatomic interactions in shaping real-space and momentum-space structures. The competition between lattice depth and interaction strength gives rise to a rich phase diagram of ground-state configurations. In the absence of Raman coupling, atoms in scalar optical lattices exhibit topologically trivial periodic density distributions without forming vortices. When only Raman coupling exists, a regular array of vortices of equal size will appear in one spin component, while the other spin component will remain free of vortices. Strikingly, when scalar and Raman lattices coexist, the system develops complex vortex lattices with alternating large and small vortices of opposite circulation, forming a staggered vortex configuration in real space. In momentum space, the condensate wave function displays nontrivial diffraction peaks carrying a well-defined topological phase structure, whose complexity increases with the depth of the optical potentials increasing. In spin space, we observe the emergence of a lattice of half-quantized skyrmions (half-skyrmions), each carrying a topological charge of ±1/2. These topological textures are confirmed by calculating the spin vector field and integrating the topological charge density. Our results demonstrate how the combination of scalar and Raman optical lattices, together with tunable interactions, can induce nontrivial real-space spin textures and momentum-space topological features. These findings offers new insights into the controllable realization of topological quantum states in cold atom systems.