"З Новим Роком вас!"

Translation: Happy New Year to you!

[Chalseadagger]

Does "З" in this sentence has the same function as in "з пасхою"?

[deactivated user]

Right!

It’s a short for «Віта́ю з Нови́м Ро́ком» ‘I congratulate [you] upon the New Year’. English ‘congratulate’ requires ‘upon’, while Ukrainian «віта́ю» requires «з». It’s not the usual meaning of «з», it’s just the preposition used in this construction.

[Pea44]

Its sounds strange in russian