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A search for exotic Higgs boson decays H → AA, with A → YY is presented, using events with a semi-merged topology. One of the hypothetical particles, A, is assumed to decay promptly into a semi-merged diphoton system reconstructed as a single photon-like object, while the other A decays into two resolved photons. The search is performed using proton-proton collision data collected by the CMS experiment at s=13 TeV, corresponding to an integrated luminosity of 138 fb−1. The data agree with the standard model background expectation. Upper limits are set on the product of the Higgs boson production cross section and the branching fraction, σ(pp → H) B(H → AA → 4γ), which range from 0.264 to 0.005 pb at 95% confidence level, for A masses in the range 1 < mA< 15 GeV. These limits are the most stringent to date in the 1–5 GeV mA range.