Let L=−ΔHn+V\documentclass[12pt]{minimal}
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\begin{document}$L=-\Delta_{\mathbb{H}_{n}}+V$\end{document} be a Schrödinger operator on the Heisenberg group Hn\documentclass[12pt]{minimal}
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\begin{document}$\mathbb{H}_{n}$\end{document}, where the nonnegative potential V belongs to the reverse Hölder class RHq1\documentclass[12pt]{minimal}
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\begin{document}$RH_{q_{1}}$\end{document} for some q1≥Q/2\documentclass[12pt]{minimal}
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\begin{document}$q_{1} \ge Q/2$\end{document}, and Q is the homogeneous dimension of Hn\documentclass[12pt]{minimal}
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\begin{document}$\mathbb{H} _{n}$\end{document}. Let b belong to a new Campanato space Λνθ(ρ)\documentclass[12pt]{minimal}
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\begin{document}$\Lambda_{\nu }^{ \theta }(\rho )$\end{document}, and let IβL\documentclass[12pt]{minimal}
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\begin{document}$\mathcal{I}_{\beta }^{L}$\end{document} be the fractional integral operator associated with L. In this paper, we study the boundedness of the commutators [b,IβL]\documentclass[12pt]{minimal}
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\begin{document}$[b,\mathcal{I}_{\beta }^{L}]$\end{document} with b∈Λνθ(ρ)\documentclass[12pt]{minimal}
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\begin{document}$b \in \Lambda_{\nu }^{\theta }(\rho )$\end{document} on central generalized Morrey spaces LMp,φα,V(Hn)\documentclass[12pt]{minimal}
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\begin{document}$LM_{p,\varphi }^{\alpha ,V}(\mathbb{H}_{n})$\end{document}, generalized Morrey spaces Mp,φα,V(Hn)\documentclass[12pt]{minimal}
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\begin{document}$M_{p,\varphi }^{\alpha ,V}(\mathbb{H}_{n})$\end{document}, and vanishing generalized Morrey spaces VMp,φα,V(Hn)\documentclass[12pt]{minimal}
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\begin{document}$VM_{p,\varphi }^{\alpha ,V}(\mathbb{H}_{n})$\end{document} associated with Schrödinger operator, respectively. When b belongs to Λνθ(ρ)\documentclass[12pt]{minimal}
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\begin{document}$\Lambda_{\nu }^{\theta }(\rho )$\end{document} with θ>0\documentclass[12pt]{minimal}
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\begin{document}$\theta >0$\end{document}, 0<ν<1\documentclass[12pt]{minimal}
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\begin{document}$0<\nu <1$\end{document} and (φ1,φ2)\documentclass[12pt]{minimal}
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\begin{document}$(\varphi_{1},\varphi_{2})$\end{document} satisfies some conditions, we show that the commutator operator [b,IβL]\documentclass[12pt]{minimal}
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\begin{document}$[b,\mathcal{I}_{\beta }^{L}]$\end{document} is bounded from LMp,φ1α,V(Hn)\documentclass[12pt]{minimal}
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\begin{document}$LM_{p,\varphi_{1}}^{\alpha ,V}(\mathbb{H}_{n})$\end{document} to LMq,φ2α,V(Hn)\documentclass[12pt]{minimal}
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\begin{document}$LM_{q,\varphi _{2}}^{\alpha ,V}(\mathbb{H}_{n})$\end{document}, from Mp,φ1α,V(Hn)\documentclass[12pt]{minimal}
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\begin{document}$M_{p,\varphi_{1}}^{\alpha ,V}( \mathbb{H}_{n})$\end{document} to Mq,φ2α,V(Hn)\documentclass[12pt]{minimal}
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\begin{document}$M_{q,\varphi_{2}}^{\alpha ,V}(\mathbb{H}_{n})$\end{document}, and from VMp,φ1α,V(Hn)\documentclass[12pt]{minimal}
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\begin{document}$VM_{p,\varphi_{1}}^{\alpha ,V}(\mathbb{H}_{n})$\end{document} to VMq,φ2α,V(Hn)\documentclass[12pt]{minimal}
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\begin{document}$VM_{q, \varphi_{2}}^{\alpha ,V}(\mathbb{H}_{n})$\end{document}, 1/p−1/q=(β+ν)/Q\documentclass[12pt]{minimal}
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\begin{document}$1/p-1/q=(\beta +\nu )/Q$\end{document}.
