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GW170817 is the only gravitational-wave event for which a confirmedγ-ray counterpart, GRB 170817A, has been detected. Here, we present a method to search for another type ofγ-ray signal, aγ-ray burst precursor, associated with a compact binary merger. If emitted shortly before the coalescence, a high-energy electromagnetic (EM) flash travels through a highly dynamical and relativistic environment, created by the two compact objects orbiting each other. Thus, the EM signal arriving at an Earth observer could present a somewhat predictable time-dependent modulation. We describe a targeted search method for light curves exhibiting such a modulation, parameterized by the observer-frame component masses and binary merger time, using Fermi-GBM data. The sensitivity of the method is assessed based on simulated signals added to GBM data. The method is then applied to a selection of potentially interesting compact binary mergers detected during the second (O2) and third (O3) observing runs of Advanced LIGO and Advanced Virgo. We find no significant modulatedγ-ray precursor signal associated with any of the considered events.