I moved from PA to NJ for new job on Nov'19. spouse in WA all year. what is my filing status-MFJ/MFS in state? and how/where to allocate 1099 INT and child(age 3) credit?

[KathrynG3]

In general, New Jersey expects your filing status to match the Federal filing status. See NJ-1040 Instructions, page 7.

Allocate income based on where you were living when you received it. 

First, in the My Info section, be sure to fill out all details for dates of residency for each spouse. (Scroll towards the bottom of your details.)

While you will not have any filing requirement in Washington, you will have to file a return for Pennsylvania and New Jersey. Start by entering Pennsylvania before you enter New Jersey.