Offices under Yasa Law:
The Khan plays a very similar role to the Princes of the European domains, except that this role is exclusively reserved for members of clan Anda. There have been no non-Anda Khans in any Yasa domain - yet.
The Tammachi position appointed by the Khan and directly answerable to him is also exclusively open to Anda. It goes much further than the Sheriff role of Europe - it is more like a mix of a military commander and the head of the military police, a more militaristic form of a Seneschal. Unless the Khan actively intervenes and takes the matter personally over, the Tammachi is in charge of organizing the Anda of lower rank and raising, leading and dismissing any Alginchi, enforcing the Yasa on the other vampires, and ensuring the peace and security of the domain.
In times of war directly affecting the domain (vampiric or human), all military matters are directed by Tammachi - and this includes rationing and distributing Herds, Resources, Retainers and other assets relevant for the war effort.
The Daruqachi office is the first office open to others than Anda - in fact, it is almost always given to a member of an outsider clan. The Daruqachi is appointed by and directly answerable to the Khan. His role is most comparable to an European Seneschal - but he holds no direct power over Anda. The Daruqachi is there to govern the other members of the outsider clans. While the Khan could take over matters personally, he is usually content to let the outsiders deal with their own matters themselves.
The Alginchi role appointed by the Tammachi is unique to the Mongol Yasa. Translating it as "scout" is a bit misleading, as in the mortal Mongol army "scouts" are elite soldiers directly answerable to their Tammachi general, commandos that sneak alone or in pairs behind enemy lines, gather intelligence and engage in opportunistic coups de main. They are more like a mix of a Scourge and a more limited Sheriff, scouting the area for unbidden guests and other threats, enforcing the Yasa law and the Sheriff's orders in absence, and opportunistically engaging with other threats to the military order and security of the domain. They don't hold special authority over other Anda (in fact, the Alginchi role is also open to outsiders), nor can they seize things under a state of emergency, except when carrying out the Tammachi's order to do so on his behalf.
The Jarquchi are the aides of the Daruqachi, members from outside clans appointed by the Daruqachi. While being a "judge" is the traditional job of a Jarquchi (and they all may be called up to settle a dispute between two non-Anda*, if all involved parties can agree to work through him and be bound by his verdict), the potential roles can vary much further, as decided by the Daruqachi - chronicler, scribe, census-taker, bureaucrat. As the vampire society grows in size and complexity, the Khan and/or Daruqachi may decide to formalize and define these sub-specialties to better order their fief, or to add other offices only known in outside lands like that of the Harpy, but for now, this rough order seems to do.
*Anda are notably not bound to the verdicts of a Jarquchi or even a Daruqachi - and even if they agree to have a matter mediated by them, they can always appeal to the Tammachi or Khan to overrule them.
Etiquette:
Matters of etiquette at the courts of the steppe barbarians are both much simpler and almost scandalously meritocratic by European standards. Office holds much greater bearing than age - an office-less Ventrue Elder would have to bow to an Anda Neonate Alginchi, an almost obscene idea to a vampire not immersed in the Mongol culture of the Yasa.On the other hand, the offices of Daruqachi and Jarquchi receive very little respect by Anda, and the culture of the applied Yasa bolsters them in this assessment. The two outsider offices are seen as useful, even commendable if they do their jobs well, but they don't hold the same importance as other Anda, and especially not the same as Anda-exclusive offices.
If differences in office don't apply, age is the next deciding factor, but to a smaller degree than in Europe: