Would I have to pay Yonkers income tax if i move to a Scarsdale PO in Yonkers?

If you work and/or live in a location (for example, Yonkers), you are generally subject to taxation at that location. This is true for all taxing authorities e.g. City, County, School District, State, etc.

If you merely have a Post Office box at a location because it is convenient for you, that does not constitute establishing residence and you should not owe taxes as a result.

Scarsdale PO homes are homes with the 10583 zip code but are located outside the Town and Village of Scarsdale.  These areas include homes in Eastchester, Edgemont, Town of Mamaroneck, New Rochelle and Yonkers. 

If your home is in Yonkers, you are subject to the Yonkers City income tax