Dvoyka, in a word, is the "Commission for Internal Affairs under Comrade Yeshov and the USSR public prosecutor, Comrade Vyshinskiy".
This Dvoyka operated as out of court organ; during the Great Terror period it pronounced judgements in the absence of the persons concerned. The Dvoyka, in contrast to the other out-of-court or quasi-court organs of the Communist "legal system", exclusively imposed "VTM" (DEATH BY FRING SQUAD = maximum penalty).
Sometimes (in 2-3% of the cases) the Dvoyka verdict was later-on amended into camp imprisonment, imposed by the "special assembly".
The functioning of this Dvoyka was officially explained with the fight against anti-Soviet (foreign) spies and saboteurs. In our region the Dvoyka formally legalized the files of Poles, Germans, Estonians, Latvians, Lithuanians, Chinese and Koreans, as well as Finns and even Kharbines ("Kaveshdines", i.e. former workers from the KVShD (= Chinese-Eastern Railroad), who had returned from Mandchuria. Each of these categories was subject to a certain PREDETERMINED QUOTA, imposed by the NKVD in Moscow.
These "Kharbines" would occasionally appear in the files as ethnic Poles, Germans or Estonians, but once they had been officially registered as "Kharbines", they were reported to be Japanese spies (like the Chinese and Koreans). In the remaining cases Poles were registered as Polish spies (or "members of nationalist organizations, who had been in contact with the Polish intelligence service"), the Estonians as Estonian spies, etc.
In some cases the Dvoyka did not declare Poles and members of other minorities as being "spies", but accused them of having committed a punishable offence as defined by §58-10 ("ASA" (= anti-Soviet agitation) or "KRA" (= counter-revolutionary agitation)). The final decision, however, remained the same: VMN (= maximum penalty = death by firing squad).
It obviously happened from time to time that the number of ethnic Poles was not enough in order to fulfill the planned quota - in this case they registered Belorussians as Poles. Or, in case ordinary Russians, who could somewhere, somehow be connected with a relationship to Poles, fell into the hands of the Dvoyka, they simply wrote: married to a Polish woman. Or they patched up the predetermined target for Jews by adding a note for the records of those who were born in Baranovitch or Vilna: "Polish military organization".
However, it also happened that ethnic Finns, Lithuanians, Poles were not arrested by the Dvoyka, but by the "usual" Troyka.
In some regions the NKVD additionally "took up" further Dvoyka categories. Thus, there was a planned quota for "zionists" in Ukraina (which was fulfilled, as a matter of fact).