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This study reports five types of metal-doped (Co, Cu, Sn, V, and Zr) NASICON-type Li_1.3Al_0.3Ti_1.7(PO₄)₃ (LATP)/polymer composite solid electrolytes (CSEs) enabling Li₄Ti₅O₁₂ (LTO) anodes to have high rate capability and excellent cycling performance. The high Li⁺-conductivity LATP samples are successfully synthesized through a modified sol–gel method followed by thermal calcination. We find that the cation dopants clearly influence the substitution of Al for Ti, with the type of dopant serving as a crucial factor in determining the ionic conductivity and interfacial resistance of the solid electrolyte. The CSE containing poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP), lithium bis(trifluoromethanesulfonyl)imide (LiTFSI), and Sn-LATP shows an ionic conductivity of 1.88 × 10⁻⁴ S cm⁻¹ at ambient temperature. The optimum conductivity can be attributed to alterations in the lattice parameters and Li⁺ transport pathways owing to Sn doping. The solid-state cell equipped with the LTO-supported CSE containing Sn-LATP fillers demonstrates both excellent high rate capability at 5 C (with a capacity retention of 86% compared to the value measured at 0.2 C) and superior cycling stability, maintaining high Coulombic efficiency (>99.0%) over 510 cycles. These findings indicate that the proposed CSE is highly promising for use in solid-state lithium batteries with desirable charge–discharge properties and high durability.