Localized kinetic-scale regions of strong current are believed to play an important role in plasma thermalization and particle acceleration in turbulent plasmas. We present a detailed study of a strong localized current, 4900 nA m(-2), located at a fast plasma jet observed in the magnetosheath downstream of a quasi-parallel shock. The thickness of the current region is similar to 3 ion inertial lengths and forms at a boundary separating magnetosheath-like and solar wind-like plasmas. On ion scales the current region has the shape of a sheet with a significant average normal magnetic field component but shows strong variations on smaller scales. The dynamic pressure within the magnetosheath jet is over 3 times the solar wind dynamic pressure. We suggest that the current sheet is forming due to high velocity shears associated with the jet. Inside the current sheet we observe local electron acceleration, producing electron beams, along the magnetic field. However, there is no clear sign of ongoing reconnection. At higher energies, above the beam energy, we observe a loss cone consistent with part of the hot magnetosheath-like electrons escaping into the colder solar wind-like plasma. This suggests that the acceleration process within the current sheet is similar to the one that occurs at shocks, where electron beams and loss cones are also observed. Therefore, electron beams observed in the magnetosheath do not have to originate from the bow shock but can also be generated locally inside the magnetosheath.