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Measurements of >82 MeV Galactic cosmic-ray (GCR) protons at Earth indicate that they may be mixed with protons that leak into the heliosphere from Jupiter’s magnetosphere (Jovian cosmic-ray protons (JCRPs)). A ∼400 day periodicity in these proton fluxes, which is similar to the synodic period between Jupiter and Earth, and an excess proton flux observed when Jupiter and Earth can be connected through the interplanetary magnetic field were the basis for this claim. Using nearly 13 yr of GCR measurements at Saturn with Cassini’s Magnetosphere Imaging Instrument, we show that the ∼400 day periodicity is also present in ≳100 MeV protons at ∼9.6 au, although the synodic period between Saturn and Jupiter is ∼20 yr. We also find that the features responsible for this periodicity were convected from 1 au to Saturn’s distance with the solar wind velocity. Their origin is therefore heliospheric, not Jovian. We attribute these features to quasi-biennial oscillations, observed in the solar magnetic field and various heliospheric indices. This finding indicates that fluxes of JCRPs at 1 au, if present, are considerably overestimated, because the signal originally attributed to them represents the amplitude of the ∼400 day periodic GCR oscillation. This oscillation has to be subtracted before the resulting proton GCR flux residuals are analyzed in the context of a possible Jovian source. A confirmation of the presence of JCRPs over extended regions in the heliosphere and a constraint on their fractional abundance in GCR spectra may therefore require further validation and analysis, and several options are proposed for this purpose. [ABSTRACT FROM AUTHOR]