1930 US Census
Clifton, Passaic Co., New Jersey
Zuakouskey, Anton, Head, aged 37, married, aged 21 at first marriage, b. Poland (Slovak), parents b. same, immigrated 1913, carpenter, railroad car manufacturer
Zuakouskey, Mary, Wife, aged 43, married, aged 17 at first marriage, b. Czechoslovakia (Slovak), parents b. same, immigrated 1905
Zuakouskey, Mary, Daughter, aged 23, b. New Jersey
Zuakouskey, Caroline, Daughter, aged 13, b. NJ
Zuakouskey, Helen, Daughter, aged 11, b. NJ
Zuakouskey, Emil, Son, aged 5, b. NJ
Lischuk, Joseph, Boarder, aged 40, married, b. Poland (Slovak), parents b. same, immigrated 1913, salesman, furniture store
Anton is not Mary's father, given her age, so is likely Mary's daughter from a first marriage.
I have checked the Buffalo crossing records and can find no record of his crossing in the time period you mention.