A generic search for a low mass dilepton resonance in Higgs boson decays is conducted in the four-lepton final state. The decay is assumed to proceed via two new particles (beyond the standard model), or one new particle in association with a Z boson. The search uses proton-proton collision data collected by the CMS detector, corresponding to an integrated luminosity of 137~\mathrm{fb}^{-1}, at a center-of-mass energy \sqrt{s}=13~\mathrm{TeV}. No significant deviation from the standard model expectation is observed. Upper limits at $95\%$ confidence level are set on model-independent cross sections and Higgs boson decay branching fractions. Additionally, limits on dark photon and axion-like particle models are reported. $\textit{This document has been revised with respect to the version dated May 26, 2020.}$

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