Nonlocal quantum fractional partial with variable coefficients appear in the modeling of complicated systems that are ruled by long range nonlocal interactions, memory effects, anomalous diffusion, heterogeneous media, and quantum scale dynamics. The numerical solution of these systems is difficult because of the dense algebraic structures generated by fractional operators; long-range interactions which have global coupling due to the global nature of the nonlocal kernel; and variable coefficients introduce local irregularities that can only be accurately resolved with uniform discretization. To provide an accurate and reliable approximation of nonlinear nonlocal QT PDEs with variable coefficients, this study proposes a Certified Structure-Preserving Adaptive Spectral-Finite Element Method (CSPA-SFEM). This method utilizes the high order accuracy of spectral approximations via fractional methods, coupled with the geometric flexibility and local refinement potential of finite element discretization. A midpoint and discrete gradient structure-preserving time integration scheme is employed to preserve the fundamental invariants of the QT system, including discrete mass and Hamiltonian energy. Additionally, an estimate of the a posteriori error in multiple components (i.e., spatial residual error, spectral truncation error, temporal error, coefficient approximation error, quadrature error and error due to approximating the nonlocal kernel) is provided to measure their respective contributions to a unified adaptive framework. The adaptive scheme uses a solve–estimate–mark–refine/enrich–update approach, enabling simultaneous refinement of the mesh and spectral mode enrichment, based on dominant error source. Theoretical analysis shows that the discrete problem is well posed, has preserved discrete invariants, converged to fully discrete scheme, and was both reliable and efficient concerning the proposed estimator. Numerical experimentation demonstrated (i) stable evolution of wave functions, (ii) optimal convergence behavior, (iii) reliable error estimation, (iv) effective localization of error(s), (v) preserved mass, (vi) preserved energy, and (vii) improved computational efficiency compared to uniform refinement of meshes. These results indicate that the CSPA-SFEM provides a certified, accurate and physically consistent framework for long term computational simulation of nonlinear nonlocal quantum–fractional systems in heterogeneous material media.