In short, we don't know, as is the case with a substantial number of the coats of arms. This is largely due to the scarcity of written materials and relatively late attempts at codification that happened in Poland only around late 15th century. Relative simplicity of the coat of arms that consists of four figures that can be easily represented with lines suggests its relatively old age and Central European origin (Western Europeans commonly used field division and natural depictions of animals and other elements while Eastern Europe favoured usage of linear marks, similar to Central Asian tamgas, although these are not hard-and-fast rules).

The coat of arms is first mentioned in the Polish Chronicle of Jan Długosz, who mentions the family 'Dragovie alias Sassovie', describing their coat of arms as 'In blue field, a moon yellow or golden, with each of the corners pointing to a golden star, in the middle of the moon an arrow pointing upwards', attributing its origin to dukes of Wallachia. It is worth noting that this first depiction of the coat of arms refers to the variant known in modern heraldry as 'Sas', identical to one used by Hungarian family Dragffy.

It is very likely, however, that the Sas coat of arms indeed originated somewhere in northern Hungary, possibly in Transylvania or Maramureș region, as the holdings of noble families that used it were concentrated in southern Galician Ruthenia (southeastern part of modern Poland and southwestern part of modern Ukraine), making it very possible that it originated among Wallachian nobility that was later invited around 14th century to southern Lithuania, possibly in an attempt to bolster the power of the latter in the ongoing struggle with Teutonic Order. In addition, with the threat posed by the Tatars in the southeast, Polish rulers in 14th and 15th century additionally granted lands in Ruthenia to strengthen the defenses against Tatars.

The colonization of the area by Wallachian nobles was usually based on the Wallachian law, separate from Polish, German or Ruthenian legal systems. It is speculated that many members of lower Wallachian nobility moved to Ruthenia and being relatively unknown and not being granted land, they entered the service of other nobles, often adopting their coat of arms, leading to the proliferation of the members of the Drag-Sas family that quickly became a dominant one in the region. Sas family quickly grew in the Red Ruthenia and according to the census of the Ruthenian nobility made under the supervision of Jan Zamoyski in 1427 for the purposes of the royal homage ceremony, out of 480 representatives of the nobility from the aforementioned region, more than 140 belonged to various branches of that family.

Given that the name 'Sas' is very similar to a name of the son of Dragoș I, prince of Moldavia and voivode of Maramureș and that the coat of arms was associated with the Hungarian family Dragffy that is considered a Hungarian variant of the name Dragoșești (descendats of Dragoș), many historians suggests that it has Moldavian or Transylvanian origin. Theory suggesting relation between the name 'Sas' and saxons (pol. 'Sasi', sing. 'Sas') is generally considered to be false, as there is no indication that Saxon inhabitants of Transylvania were represented to any extent among the members of the Sas family in Ruthenia, and given the prevalence of said family, such observations would have certainly been made (especially given that many of the Wallachian nobility was invited by Polish rulers specifically to help in resisting largely German-speaking inhabitants of Teutonic State). One could, however, derive the name of the coat of arms from the German colonists in southeastern Poland who located many villages in the area, but this does not explain why Sas coat of arms is identical to one used by Hungarian family Dragffy.

It is worth noting that precise origin of the new settlers is very hard to ascertain, as e.g. holder of the lands near the Wiarem river was referred as 'Stefan the Hungarian of Rybotycze' in royal beneficium act of 1367, although the same noble defines himself as 'Stefan Rybotycki the Wallachian' in a land sale document of 1359 (the former document uses the word 'dictus' (lat. 'called') meaning that 'Hungarian' might have been a nickname given to him by others. Thankfully, in this particular case we know who was the person described above. It is very possible that he was originator of the house of Sas in Poland and the coat of arms is indeed derived from the 'son of Sas', as Stefan was son of aforementioned Sas, ruler of Maramures and grandson of Dragoș. Document issued in 1355 by king Louis I of Hungary who donated lands around Konyha to Sas and his sons mentions four of the latter: Balc, Drag, Dragomir and Stefan. The next such document, issued in 1373, some time after Sas's death, mentions only Balc, Drag and Janos (Dragomir perished in the battle in 1365). Given that 'Stefan the Hungarian/Wallachian' has received lands from in Ruthenia from Polish king Kazimierz III prior to 1359, it strongly suggests that Stefan, son of Sas, left Maramures for Ruthenia to enter the service of Polish king somewhere between 1355 and 1359, bringing with him the coat of arms.

A common story presented in the armorial written by Kasper Niesiecki, 18th-century Polish Jesuit scholar, links the families using Sas and Vukry coat of arms with the figure of Vancha the Wallachian (ukr. Vancha Voloshyn, Vanchalukh), sometimes presented as 'count' who is said to receive the land in Ruthenia around 1431 and whose sons (Ivanko, Khodko and Zanko) also received beneficium in the area, namely the villages of Ilnik, Turka and Jawor, thus beginning the families of Ilniccy, Turscy/Tureccy and Jaworscy respectively. 'Vancha' is most likely a reference to a person referred to as 'Ivan Olachus', son of Dragomir and grandson of Sas (and a nephew of Stefan the Hungarian/Wallachian), in the beneficium act of 1387, when said man received land in Iza and Also Apsa in Maramureș region from the king Sigismund of Luxembourg. Niesiecki also suggests that the coat of arms originated in Saxony and thus it is called 'Sas', but today it is considered a mere coincidence, given that the word 'Sas' (read 'shash') exists also in Hungarian, where it means 'eagle'. Please note that Niesiecki's version of the origin of Sas coat of arms is sometimes referred to as a 'legend', but it is backed by a sound evidence and it is perfectly possible that both Ivan and Stephen, who were closely related, could have independently brought their own seals or coats of arms to Ruthenia.

Another legend derived Sas coat of arms from a literal Sas, i.e. a Saxon noble Hyyd or Huyd who came from Saxony to Hungary and later to Galicia, where he entered the service of Leo I of Halich and Volodimir and settled somewhere in southern Ruthenia. This story is present in the book 'Herby Rycerstwa polskiego' (Coat of arms of Polish knights) written by Bartosz Paprocki and first published in 1584. Author attributes the origin of this information to an earlier chronicle of Wojciech (Adalbert) Strepa, but so far, the existence of the latter document document has not been corroborated by any evidence. It has never been found or referenced anywhere else in the capacity other than the quote from Paprocki and other information attributed to Strepa have been later found to be false, strongly suggesting that the alleged chronicle is completely fictitious (some of them are thought to be slightly altered informations sourced from other existing documents, e.g. Chronicle by Jan of Czarnków). It is worth mentioning though, as many earlier historians up to early 20th century treat Strepa's chronicle as a real source, with Ludwik Wyrostek being possibly the first who suggested in 1932 that this might not be the case.