This thesis presents a search for the rare Higgs boson decay, H → Zγ, where Z → ℓ+ℓ− and ℓ = electron or muon. According to the Standard Model, this decay process involves quantum loops, which implies its small branching fraction compared to tree-level processes. The search is performed on the proton-proton collision data from the Large Hadron Collider (LHC) at the center-of-mass energies of 13 TeV and 13.6 TeV, recorded by the Compact Muon Solenoid (CMS) experiment with a total integrated luminosity of 200 fb^(−1). To maximize sensitivity, multiple Higgs boson production modes are targeted. Events in different modes are further classified into multiple categories, using machine-learning-based or cut-based selections on physics variables. The signal is extracted from a simultaneous fit of parametric models over the invariant mass distributions of the ℓ+ℓ−γ system from all the categories. To ensure accurate modeling of distributions and minimal bias, the background models are rigorously tested. The observed signal strength μ relative to the Standard Model prediction is found to be μ = 1.10(+0.52/−0.61) for a Higgs boson mass at 125.38 GeV. The statistical significance of the measurement is 1.9 standard deviations.