Jaškin could have played in the 2011 IIHF World U20 Championship, but suffered a knee injury in an Extraliga game on 21 November, which sidelined him for six weeks and caused him to miss the tournament.

[8] Jaškin as a free agent from the Capitals, opted to pause his NHL career and returned to Russia in signing a one-year deal with HC Dynamo Moscow of the KHL on 22 August 2019.

[10] After two highly productive seasons with HC Dynamo Moscow, Jaškin returned to North America as a free agent, agreeing to a lucrative one-year, $3.2 million contract with the Arizona Coyotes on July 28, 2021.

As a free agent, Jaškin returned to the KHL and was signed to a one-year contract after his rights were traded from Dynamo Moscow to SKA Saint Petersburg on 25 July 2022.

On 7 June 2023, Jaškin as the top tier free agent of the league was signed to a three-year contract with SKA competitor club, Ak Bars Kazan.