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Neutral sodium (Na i ) is an alkali metal with a favorable absorption cross section such that tenuous gases are easily illuminated at select transiting exoplanet systems. We examine both the time-averaged and time-series alkali spectral flux individually, over 4 nights at a hot Saturn system on a ∼2.8 day orbit about a Sun-like star WASP-49 A. Very Large Telescope/ESPRESSO observations are analyzed, providing new constraints. We recover the previously confirmed residual sodium flux uniquely when averaged, whereas night-to-night Na i varies by more than an order of magnitude. On HARPS/3.6 m Epoch II, we report a Doppler redshift at v _Γ,NaD = + 9.7 ± 1.6 km s ^−1 with respect to the planet’s rest frame. Upon examining the lightcurves, we confirm night-to-night variability, on the order of ∼1%–4% in NaD, rarely coinciding with exoplanet transit, not readily explained by stellar activity, starspots, tellurics, or the interstellar medium. Coincident with the ∼+10 km s ^−1 Doppler redshift, we detect a transient sodium absorption event dF _NaD / F _⋆ = 3.6% ± 1% at a relative difference of Δ F _NaD ( t ) ∼ 4.4% ± 1%, lasting Δ t _NaD ≳ 40 minutes. Since exoplanetary alkali signatures are blueshifted due to the natural vector of radiation pressure, estimated here at roughly ∼−5.7 km s ^−1 , the radial velocity is rather at +15.4 km s ^−1 , far larger than any known exoplanet system. Given that the redshift magnitude v _Γ is in between the Roche limit and dynamically stable satellite orbits, the transient sodium may be a putative indication of a natural satellite orbiting WASP-49 A b.