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We conduct a comprehensive search for transiting exomoons and exosatellites within 44 archival Spitzer light curves of 32 substellar worlds with estimated masses ranging between 3 and 30 M _Jup . This sample’s median host mass is 16 M _Jup , inclusive of 14 planetary-mass objects, among which one is a wide-orbit exoplanet. We search the light curves for exosatellite signatures and implement a transit injection-recovery test, illustrating our survey’s capability to detect >0.7 R _⊕ exosatellites. Our findings reveal no substantial (>5 σ ) evidence for individual transit events. However, an unusual fraction of light curves favor the transit model at the 2–3 σ significance level, with fitted transit depths consistent with terrestrial-sized (0.7–1.6 R _⊕ ) bodies. Comparatively, fewer than 2.2% of randomly generated normal distributions from an equivalent sample size exhibit a similar prevalence of outliers. Should one or two of these outliers represent a real exosatellite transit, it would imply an occurrence rate of $\eta ={0.61}_{-0.34}^{+0.49}$ short-period terrestrial exosatellites per system, consistent with the known occurrences rates for both solar system moons and mid-M dwarf exoplanets. We explore alternative astrophysical interpretations for these outliers, underscoring that transits are not the only plausible explanation. For orbital periods <0.8 days, the typical duration of the light curves, we constrain the occurrence rate of sub-Neptunes to η < 0.35 (95% confidence) and, if none of the detected outlier signals are real, the occurrence rate of terrestrial (∼Earth-sized) exosatellites to η < 0.51 (95% confidence). Forthcoming JWST observations of substellar light curves will enable the detection of sub-Io-sized exosatellites, allowing for much stronger constraints on this exosatellite population.