The purpose of this study is to investigate the dust ion-acoustic soliton (DIAS) structures in a magnetised plasma with superthermal components in the presence of trapped electrons, positive (negative) ions and opposite charged dust particles. Using the well-known reductive perturbation technique and a hydrodynamic model for ions, we have constructed both the Schamel Zakharov–Kuznetsov (S-ZK) and Schamel Korteweg–de Vries (S-KdV) equations. An energy integral equation involving Sagdeev’s pseudopotential is derived and the fundamental properties of small-amplitude solitary waves are investigated. The implications of relevant plasma parameters, such as the spectral index parameter, trapped electron parameter, positive (negative) dust number density and ion cyclotron frequency, on the profile of the Sagdeev’s pseudopotential and the corresponding solitary waves are shown graphically.