Yes Canadian Geese are protected federally in all USA states including New York.
If you kill a Canadian Goose or Canadian Geese and are caught you can face fines and or prison or jail time unless you have a permit to kill the Canadian Goose.
Getting a permit is not very easy though and very unlikely for most people to get.
Canada geese are a federally protected species under the Migratory Bird Treaty Act and you could face prison time and or fines for killing a Canada goose.
That is unless you have a permit to kill the goose that is causing issues but you would have to get the permit and have a very good reason to legally kill the Canada Goose.
If you do need to repel Canada Geese you can use humane repellency methods such as dogs, lasers or other frightening techniques to get rid of the Canada Geese.
As for other geese you might be able to legally kill the geese during hunting season but usually not before then.