There were a couple. Most of the sourcing for this comes from Geoffrey Hosking's Russia and the Russians (https://www.amazon.com/Russia-Russians-History-Geoffrey-Hosking/dp/0674004736).

The first change came with the coming of the Mongols and their domination. The Princes of Rus, as there was no Russian state yet, had to take themselves "to the Horde" to receive the iarlyk from the Golden Horde. This affected the class relations of 14th century Russia because the Princes were encouraged to be as extractive as possible in their dealings with the peasants who lived on their land. This means that they fully subjugated the Myr or village council of the peasants on their land. This was a period where there were not really local levies, each prince had a retinue or Druzhina as his fighting men and that served as an army.

The second set of changes comes in the late 14th century as the golden Horde collapses and Muscovy and Moskova assume control. We see a number of principalities band together and defeat the steppe nomads. This was a significant moment as it demonstrated Moscow's ability to resist the Tatars. As Ivan the 4th centralized muscovy and pushed it outward the Cossacks, essentially leftover Tatars of various tribes threatened the new muscovite borderlands. Ivan the 4th managed to draw the Cossacks of the Don river basin into an alliance.

Additionally, when Ivan the third was"Gathering the lands" and subjugating errant principalities, particularly Novgorod and Pskov, he expelled their nobles and split up the Udels to make up the Pomieste or the start of a service estate.

TL:DR While there were changes in the middle ages, but the Mongols were not the direct causes of them necessarily. I hope this answers your question. Edit: Paragraphs