The Ekosian SS are an antagonistic faction of hostile human-like aliens in Star Trek: The Original Series. Under the command of the genocidal Melakon, they became brutal and hateful agents of his will who took delight in torture and execution.
Unlike many other Ekosians, they also happily took to outright genocide against the Zeon minority and were a dark parallel of the SS from Earth (who they likely idolized, much as Melakon idolized Hitler).
With the death of Melakon and the end of his genocidal campaign, it is likely the current Ekosian SS was disbanded and punished for their crimes - however, it is possible that they still exist under a new name and function as the Ekosians did not entirely give up Nazism despite the horrors it had unleashed upon them.
As well as the SS, there existed an Ekosian SA - which were shown to engage in similar brutality.
The Ekosian SS and Ekosian SA are based upon the troops utilized in Nazi Germany during the persecution of the Jews (and other "unwanted" members of society) - this coupled with Starfleet officers disguising themselves as Nazi officers made this one of Star Trek's most controversial episodes.
The Ekosian SS seemed to follow the same pseudo-science as many Nazi scientists, such as when they commented on Spock as an inferior being due to his Vulcan features (in Nazi Germany, many tried to base race inferiority on superficial physical traits, often petty, such as stereotypes of large nosed Jews).
The topic of Nazi aliens returned with Enterprise and introduced Vosk and his allies, who were aiding Earth's Nazi Germany thanks to time-travel.