<p>Constructing a physically realizable fractional-order random walk model within finite spaces and heterogeneous potential fields has long remained a persistent challenge in the study of anomalous diffusion. In this paper, a novel composite continuous-time random walk model is investigated to characterize anomalous diffusion in a potential field over a finite domain under non-Markovian temporal conditions, in which the composite jumps that incrementally sample spatial forces are considered for the trapped particles in potential field. Concurrently, we consider both biexponential and power-law waiting time distributions to capture trapping effects in complex environments. In the continuous limit, we rigorously derive the macroscopic evolution equations corresponding to the master equation of this random walk: a spatial fractional Fokker-Planck equation for biexponential waiting times and a time-space fractional Fokker-Planck equation for power-law waiting times. Here, the spatial fractional derivative is defined via spectral fractional Fokker-Planck operator, endowing it with a clear physical interpretation in finite domains; the time fractional derivative takes the Caputo form, characterizing the non-Markovian nature of power-law waiting times. We derived the analytical solution of the propagator for the diffusion equation under reflecting and absorbing boundary conditions, and conducted a discussion on the first-passage time under double absorbing boundaries within a finite domain. By comparing the analytical solutions of the propagator and first-passage time probability density function with Monte Carlo simulation results, we validated the correctness of the theoretical derivation. This model may hold significant value for understanding complex transport processes.</p>