Throughout English history, the word subpoena has been alternatively spelled subpœna, suppena, and subpena. However, all of this traces back to the Latin sub poena, which meant "under penalty". This phrase was adopted into English common law in 1623 under James I as a legal term for a summons, and it's been used by many countries since then. So, subpoena is a bit of a literal translation: sub- means "under", and poena meant "penalty". Sub-, through Proto-Italic supo, comes from Proto-Indo-European upo, still meaning "under" or sometimes "below". Poena comes from Ancient Greek poine, which likewise still meant "penalty" but could also carry connotations of "fine" or "blood money", which, through several circumlocutions, comes from Proto-Indo-European key, meaning "to pay" in general. Poena, unsurprising, is also the etymon of penal and penalty, through Latin penalis. Usage of the word suubpoena in English has steadily increased since its introduction.
Adam Aleksic, a leading contender for valedictorian of his high school, is a 215-month-old boy with disturbing interests in etymology, vexillology, geography, and law. Adam would like to one day visit Tajikistan and probably isn't spying for the Uzbek government.
The Etymology Nerd