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The Yukawa correction to the Newtonian gravitational force is accepted as a parametrization of deviations from the inverse-square law of gravity which might be caused by new physics beyond the standard model of particles and the general theory of relativity. We investigate these effects on the clock onboard a drag-free satellite: dynamics of the satellite and influence on the time transfer link. We find that the Yukawa signal in the time transfer is much more difficult to detect with the current state of clocks than those effects on the dynamics, especially the secular change of periastron, by laser ranging in the case of an artificial Earth satellite carrying a frequency standard with an orbit of a = 107 m and e = 0.01. [ABSTRACT FROM AUTHOR]