It comes a little later after your era (1902-1907), but there was a movement in modern Georgia (the country) called the Gurian Republic, which was a peasant-led movement that rebelled against the Russian Empire for a couple years.
The origins of the movement stem back from the conditions in the region, which is in modern western Georgia and a very rural region, even considering the rural nature of Georgia at the time. The land was largely owned either by various nobles (many of whom were poor themselves), or the church, and peasants had to work on this land and pay taxes on it. This was also an era of considerable social change, especially within Georgia: the oil industry had began to become a major factor in the 1890s, and the first oil pipelines were built going from Baku on the Caspian Sea (now Azerbaijan) to Batumi, the major port in Georgia on the Black Sea, which is about 50km from Ozurgeti, the capital of Guria (using today's roads). Thousands of Gurians laboured in Batumi for the oil industry, and were introduced to socialist ideas (Stalin gained his first real notoriety as a socialist, but not yet Bolshevik, in Batumi around this time for his efforts in spreading propaganda). They took this information back with them to their home region, and ideas spread.
By 1902 the first real protests began, over a dispute on grazing rights. Peasants met up and agreed they'd stop paying rent to the local noble, and their actions gained the attention of some more socialist leaders, who tried to coopt the movement (though they never fully supported it: socialist theory at the time felt the peasants were not able to properly work within socialism, as they weren't developed enough for it). Further meetings kept going on, and by early 1903 nearly half of Guria was involved in this movement to boycott nobles. By 1904 the boycott extended to government and church properties, and Guria effectively forced Russian imperial authority out (not as difficult as you'd think, considering it was a rural backwater in the empire, with no vital importance). Even so, the authorities did try to restore order, arresting hundreds, but this only further their resolve, and kept spirits high.
Speaking to the form of government developed, it started on the village level: villages conducted meetings to determine legislation, and also served as de facto courts. From these village meetings they'd elect one person for every 10 households (a "tensman"), and they would further elect a "hundresman" to represent them at the larger Gurian committee. This overall committee didn't have supreme authority, which was still vested in the villages, but it served more as a liaison between them and the Georgian social democrats (who again, were a little skeptical of the whole enterprise). They also didn't have any anti-Russian sentiment, as that was not their target, just the landowners (who were mostly Georgian nobles, who themselves hated Russia for their own reasons).
As noted, the villages had their own justice, which took the form of a popular tribunal. Russian justice was incredibly corrupt during this era, so the idea of having someone judged by the entire village, in the open, was seen as a far superior system. While the death penalty existed, it was either not used or used infrequently (I can't recall specifically), but the major punishment was a boycott: the convicted person would be shunned from society, unable to talk or deal with anyone. Not surprisingly, this justice system did not work very well, as it was often used to settle personal vendettas, but it is worth noting that women were allowed to participate.
By 1905 the Gurian Republic was well entrenched, and the imperial authorities had not worried about it too much. But then Bloody Sunday happened in January 1905, when soldiers fired on demonstrators outside the tsar's palace in Saint Petersburg, protesting Russia's war with Japan (which was going terribly). Across the empire revolts and rebellions sprang up, and there was a serious threat to the empire's existence. Terrorism spread across the empire, including in Guria, where tsarist officials had remained though didn't do anything: 8 police officers were stationed there in 1905, and of them 1 was murdered, 1 wounded, 2 ran away, and the other 4 resigned. It got bad enough the Viceroy of the Caucasus cautioned the government that the Gurian movement could spread across Georgia, which was seeing a major increase in socialist agitation in light of the revolution across the empire.
A new Viceroy took office in February, and he tried to negotiate a solution, sending a representative to talk to the Gurian leadership. The conclusion of this representative were that the Gurians were too demanding, and reportedly said that the French constitution would not have been enough for them (alluding to Revolutionary France, of course).
As such a military solution was called for. This was around November 1905, and the uprisings across Russia were largely contained, except in Guria. In January imperial forces were sent to the region to pacify it, and did so brutally: hundreds of houses were burnt down, scores of people executed, more exiled or imprisoned, thousands of rubles in fines issued. But within 8 months peace and order had returned to Guria, and the Gurian Republic was no more.
That said, it was an important movement, as it led to a changing policy among Georgian socialists, many of whom were from Guria originally. They began to see that peasants could participate in their activities (not just workers), and when Georgia became an independent state between 1918-1921, they took many of these ideas and tried to use them in governing the country.
For some reading on it:
Stephen F. Jones "Marxism and Peasant Revolt in the Russian Empire: The Case of the Gurian Republic", The Slavonic and East European Review, 67 (3): 403–434.
Jones also has Socialism in Georgian Colors: The European Road to Social Democracy 1883–1917 (2005), in which he devotes a chapter to the Gurian Republic (though a lot of the information there is from his earlier article)
Alice K. Pate "Generational Conflict and the Gurian Republic in Georgia to 1905", The Soviet and Post-Soviet Review, 32 (2–3): 255–268
And I'm reluctant to do this, but the Wikipedia article on the Gurian Republic is fairly in depth, considered one of Wikipedia's Featured Articles. I will disclose that I largely wrote the article, but it is fairly comprehensive.
I assume you are talking about /r/EU4's favorite little, blue OPM, Dithmarschen! In which case, you may be interested in this previous question: