Obliquely propagating three-dimensional dust-acoustic periodic travelling waves (DAPTWs) has been undertakenin a magnetized dusty plasma composed of negatively charged inertial dust particles, trapped ions, and nonthermal fast electrons. In a dusty plasma model at hand, the dynamic behaviors of DAPTWs are governed by a Schamel equation. The presence of dust acoustic solitary waves (DASWs) and DAPTWs is investigated via bifurcation analysis of the Hamiltonian system. In the nonlinear regime, the Sagdeev potential and phase portrait structures indicate the presence of small-amplitude DAPTW solutions. The influences of intrinsic physical parameters include the strength of the static magnetic field, the obliqueness of propagation,the thermal pressure of charged dust grains, the electron to dust density ratio, the trapping parameter of trapped ions and the degree of nonthermality of fast electrons on the characteristics of DAPTWs are simulated numerically. In particular, the findings illustrate that the amplitude of DAPTWs is reduced as the numerical values of the trapping parameterare decreased. Interestingly, the numerical results of the theoretical simulations can be used to significantly highlight the physical nature of DAPTWs in astrophysical situations such as Earth’s magnetosphere, auroral region, and heliospheric environments.