Zinkovskiy was born in the present day Akmola Region in a family of a Polish descents.

Zinkovskiy was a prefect in the Major Theological Seminary in Karaganda (1998–1999) and assistant priest in the St. Joseph parish in Maikuduk (1999–2001), with the break during 2001–2003, when he studied at the Pontifical University of the Holy Cross in Rome, Italy with the licentiate of the philosophy degree.

Yevgeniy was appointed chancellor of the diocesan curia and editor-in-chief of the Kazakh Catholic magazine Credo.

In 2018, he received his Doctor of Philosophy degree from the Pontifical University of John Paul II in Kraków, Poland.

[2] On 29 April 2022 he was elected the General Secretary of the newly created Bishops' Conference of Central Asia.