I'm sure you know that one proceeds from oneself going backwards collecting documents on each generation. In few words, you need to find a Canadian document which should have a precise place of birth in UKRAINE.
Did not find anyone with a surname DZIEWERA coming to America thru NY Ellis Island. That is the spelling on a Canadian document?
In Poland [similar to your spelling] Dziawer, Dziewiarz, Dziewierz, Dziewior, Dziewiór, Dziewirz, Dziewiur, Dziewura, Dziwura.