Abstract In this paper, we investigate the motion and stability of spinning particles around a charged black hole in Bumblebee gravity. The trajectories of the particle are computed using the Mathisson–Papapetrou–Dixon equations, and the parameters of the innermost stable circular orbit (ISCO) are determined from the radial effective potential. The results show that the particle’s spin and the black hole’s parameters significantly influence the structure of the effective potential, thereby affecting the particle’s orbital dynamics and stability. Orbital simulations show that when the particle is confined within a potential well, increasing its spin or the black hole’s charge broadens the radial motion range, with the apocenter moving outward and the pericenter inward. At the same time, the Lorentz-violating (LV) parameter affects the radial motion range differently for particles with positive and negative spin. ISCO analysis further indicates that as the particle’s spin and the black hole’s charge increase, the radius, energy, and angular momentum of ISCO decrease. The effect of the LV parameter on the ISCO depends on the spin direction: increasing LV parameter for positively spinning particles brings the ISCO closer to the black hole, while negatively spinning particles exhibit the opposite trend.
Li et al. (Sat,) studied this question.