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Abstract In this work, we calculate the magnetic moments of the $$P^{N^{0}}_{\psi }$$ P ψ N 0 states and $$P^{\Delta ^{0}}_{\psi }$$ P ψ Δ 0 states with valence quark content $${\bar{c}}cudd $$ c ¯ c u d d in molecular model, diquark–diquark–antiquark model and diquark–triquark model, as well as the transition magnetic moments in the molecular model. At the same time, we also calculate magnetic moments and transition magnetic moments of $$P^{\Delta ^{++}}_{\psi }$$ P ψ Δ + + states and $$P^{\Delta ^{-}}_{\psi }$$ P ψ Δ - states in the molecular model as additional products. Our results show that in the diquark–diquark–antiquark model, the magnetic moments of $$ \lambda $$ λ excitation state are usually larger than the magnetic moments of $$ \rho $$ ρ excitation state. We find some interesting proportional relationships between the expressions of transition magnetic moments. The results provide important insights for future experimental observation of hidden-charm pentaquark states and help to distinguish their inner structures. With these efforts, our understanding of the properties for the hidden-charm pentaquark states will become more abundant.