State tax filing

Yes, I was always living in NJ however, I don’t understand what you mean by “domicile” but I did tell my employer that I moved to NYC and I had to fill out new paperwork so they withdrew nyc taxes and NY taxes only when I moved.  I was told I would get another W-2 so would have to file that also.  Then 2 months later (September), I moved back to my original place in NJ.  So I am permanently back to NJ.  So, I guess I will have to file in both states (part time in NY).  My employer said I would get three (3) W-2s.  Two for NJ which I will have to file in NJ and non-resident NYC; I would think the 2 NJ W-2s can be combined and then one for NY/NYC (part-time).  Can I file these all on turbo tax?  Can I get help when I do file this?  

Thank you.