Cosmic hydrogen reionization and cosmic production of first metals are major phase transitions of the Universe occurring during the first billion years after the Big Bang, but still poorly explored observationally. Using the JWST NIRSpec prism spectroscopy, we report the discovery of a sub-L* galaxy at zspec = 8.1623-0.0008+0.0007, dubbed RXJ2129-z8HeII, via the detection of a series of strong rest-frame UV/optical nebular emission lines and the clear Lyman break. A strong He II λ1640 emission is present, the highest redshift He II line currently known. Its high rest-frame equivalent width (EW=19.38 ± 3.24 Å) and extreme flux ratios with respect to UV metal lines and Balmer lines raise the possibility that part of RXJ2129-z8HeII's stellar populations could be Pop III-like5,6. RXJ2129-z8HeII also shows a pronounced UV continuum with an extremely steep (i.e. blue) spectral slope of β =-2.50±0.08, the steepest amongst all spectroscopically confirmed galaxies at z ≳ 7, in support of its very hard ionizing spectrum that could lead to a significant leakage of its ionizing flux7. Therefore, RXJ2129-z8HeII is representative of the key galaxy population driving the cosmic reionization. To date, this is also the most compelling case where trace Pop III stars might coexist with more metal-enriched stars.