Career
Kvasnyi is a product of the two Kyivan youth sportive schools. His first trainer was Mykola Lytovchak in Football Club Knyazha Shchaslyve. From July 2012 until 2014 Kvasnyi played in the Ukrainian Premier League Reserves for clubs Football Club Arsenal Kyiv and South Carolina Tavriya Simferopol.
From July 2014 he continued his career in the Ukrainian Premier League Reserves club Football Club Vorskla Poltava.
And in summer 2015 Kvasnyi was promoted to the main-squad team of the Football Club Vorskla in the Ukrainian Premier League. He made his debut for Vorskla Poltava in the Ukrainian Premier League in match against Football Club Dynamo Kyiv on 4 October 2015.