The verb punish came into English from the old French puniss-, extended prp. stem of punir (to punish) from the Latine punire, from poenire from poena, which is related to the Greek Ï€Î¿Î¹Î½Î® (poene; punishment, penalty).
From the same root: punishment, punishable, punitive, punitory
In modern Greek:
Ï€Î¿Î¹Î½Î®: punishment, sentence, penalty
Ï€Î¿Î¹Î½Î® (poene) - poena -> poenire -> punire -> punir -> puniss- -> punish
See the blog: English words of no apparent Greek origin at: http://ewonago.blogspot.com/