Since being a peasant was so low on the socio-economic tier, not a whole lot would change. This was a time before nationalism, so dynasties ruled over lands and people.

I can for sure say they will be responsible for the Jizya tax that non-Muslims had to pay in order to practice Christianity. It also came with other exemptions. This created a tax and political incentive to convert. Most Muslim conquests did not follow forced conversions at sword point.

Peasant boys would be at risk of being enslaved and pressed into service and converted Islam to become a Janissary. These were a class of soldiers in the Ottoman Empire that became rather influential politically.

Edit: This wasn't meant to be comprehensive of all of the changes in a Balkan Christian peasant's life, just two of the most well documented.

As Smackaroo stated The Devşirme was the system that recruited Balkan boys into the military and government.