We report observations of reconnection exhausts in the Heliospheric Current Sheet (HCS) during Parker Solar Probe Encounters 08 and 07, at 16 Rs and 20 Rs, respectively. Heliospheric current sheet (HCS) reconnection accelerated protons to almost twice the solar wind speed and increased the proton core energy by a factor of ∼3, due to the Alfvén speed being comparable to the solar wind flow speed at these near-Sun distances. Furthermore, protons were energized to super-thermal energies. During E08, energized protons were found to have leaked out of the exhaust along separatrix field lines, appearing as field-aligned energetic proton beams in a broad region outside the HCS. Concurrent dropouts of strahl electrons, indicating disconnection from the Sun, provide further evidence for the HCS being the source of the beams. Around the HCS in E07, there were also proton beams but without electron strahl dropouts, indicating that their origin was not the local HCS reconnection exhaust.