The interplay between relativistic electrons and crystalline symmetry in solids has garnered growing attention owing to their potential applications in spintronics and quantum technologies. The intertwined nontrivial topology and Rashba effect with additional control over spin degrees of freedom can coexist under the composite quantum compounds (CQCs) platform. The synergy of high-energy Rashba spin splitting (RSS) and topological surface states offers a promising coupling between electron spins and electricity. In the present study, first-principles calculations and symmetry analysis using vasp and wien2k are performed to achieve the coexistence of giant RSS, ferroelectricity, and topological phases. We investigate $X\text{GeBi}, X\text{Sn}M$ ($X$ = K, Rb, Cs; $M$ = As, Sb), and $\mathrm{CsGeS}{\mathrm{b}}_{(1-x)}\mathrm{B}{\mathrm{i}}_x$ ($X$ = 0.125, 0.25, 0.375, 0.5) compounds for potential CQCs. The CsGeBi compound is termed as intrinsic CQC with α = 4.10 eV Å while functionalized $\mathrm{CsGeS}{\mathrm{b}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}$ exhibits α = 6.89 eV Å which is a very large value among all topological materials. This work also elucidates the significant difference between vasp and wien2k relativistic band calculations such as Rashba spin splitting, unnoticed so far for surface asymmetric materials. The possible physical origin of different RSS is attributed to the different implementation methods of crystalline potential gradient in vasp (PAW) and wien2k (LAPW+lo) calculations. The findings underscore the enhanced reliability of full-potential codes in analyzing the electronic band structure of materials exhibiting surface-induced asymmetry. The spin-texture reversal corresponding to switching in polarization facilitates control and manipulation of spin degrees of freedom in these ferroelectric Rashba semiconductors. The synthesis of KSnSb, KSnAs, NaSnAs, and NaSnP offers a practical framework for guiding the synthesis of the investigated materials in current study. This research initiative unlock pathways for delving into the intertwined ferroelectricity, Rashba effect, and nontrivial topology with more reliable theoretical approaches.

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• Ferroelectricity
• First-principles calculations
• Rashba coupling
• Topological materials