Topological spin textures, like skyrmions, have significant potential for spintronics applications. The main purpose of this work is to study further the topological spin textures on the discrete lattice with magnetic fields. In this work, we study a classical rotated Heisenberg model with Dzyaloshinskii-Moriya interaction, bond-dependent anisotropy and easy-axis anisotropy on the honeycomb lattice via Monte Carlo simulations. We mainly focus on phase diagrams with magnetic fields, especially on the non-trivial phases only existing with fields. The results demonstrate the emergence of field-induced incommensurate skyrmion superlattice including mixed skyrmion-bimeron states, ferromagnetic star, vortex and z-vortex superlattice. We systematically analyze structures of these topological spin textures through spin configurations, structure factors, topological charge and vector chirality. We hope that our results could be useful for the identification of topological phases experimentally.