In Jupiter's middle magnetosphere, debate remains on the controlling physics of electron acceleration to the ultrarelativistic regime. Some local‐time asymmetric processes regulating MeV electrons may have their hold across electron spectra, leaving imprints down to 10–100s keV energies. Spectra at these lower energies can be measured with finite energy resolution, which is hardly achieved for MeV electrons. We investigate 10–100s keV electron spectra using Galileo measurements. We show that at 15–20 RJ, the power‐law exponents exhibit a previously unexpected dawn‐dusk asymmetry. This asymmetry is more prominent for 100s‐keV spectra, persistent but enhanced from 1996 to 2001. These match the theory of transport driven by a dawn‐to‐dusk electric field. Contrary to past expectations of dawn‐to‐dusk electric field at Io plasma torus (IPT) extending outward from 6 RJ, the origin of the field we infer may be completely different, despite its orientation and impacts on electron energization similar with the IPT one. Plain Language Summary: The electron radiation 5–20 Jovian radii (RJ) to Jupiter is critical as being the final baton in the relay of accelerating seed populations for the highest‐energy electrons. Trapped at <5 RJ, such harsh electron environment is the one in all within our reach strengthful enough for synchrotron emissions as those remote astrophysical sources. One essential issue in understanding the nature of this intense electron environment is quantifying its seed population distribution to discern the controlling physics among a diversity of acceleration processes. We untangle the ball of thread by resolving the time variations to establish the longitudinal and radial distributions of 10–100s keV electron energy spectra measured by Galileo spacecraft. We show that the key parameters of spectra at 15–20 RJ exhibit a previously unexpected dawn‐dusk asymmetry. This asymmetry is more prominent for 100s keV electrons, persistent but intensified from 1996 to 2001. We indicate that the featured dawn‐dusk asymmetry is possibly the global manifestation of the convective transport driven by a dawn‐dusk electric field with an origin distinct from the one discovered around 6 RJ. We suggest that this convective transport is engaged in the dynamics preconditioning the making of the innermost highest‐energy electron radiation. Key Points: The power law exponents of 100s keV electron spectra show a previously unexpected dawn‐dusk asymmetry at 15 < M < 20 in Jupiter's magnetosphereThe asymmetry intensifies from 1996 to 2001 due to the exponents' increase at dawn and simultaneous decrease at duskThe results match the theory of transport due to a dawn‐dusk electric field with an origin distinct from the one found at Io plasma torus [ABSTRACT FROM AUTHOR]