Moved from NYC to NJ midyear and worked in NJ (only) throughout the year

[StepByStep]

I believe I have to file

- Part-Year Resident Return NYC (for 1st half of yr)
- Part-Year Resident Return NJ (for 2nd half of yr)
- Non-Resident Return (NJ) (for 1st half of yr living in NYC)

I received a multipart W2 where boxes 15-17 are filled for one set of copies that includes NJ and a larger than Box 1 value for Box 16.  The second set of copies, has boxes 15-20 filled for NY, where Box 16 matches that of Box 1, and Box 18 value coincides with last paystub value for given under Taxable Wages > State Tax Taxable Wages - NY YTD value...

I do find it odd that there are taxable wages for NYC even though it was not sourced there...

I would like to know the order in which to do TurboTax states (NJ or NY first)... from which state should I be receiving credits? 

From (https://ttlc.intuit.com/turbotax-support/en-us/help-article/printers-printing/file-part-[product key...) I started with NY first and now doing NJ after...  For NY then, should I add anything for the step Take a look at New York credits and taxes > Credit for Taxes Paid > Taxes Paid to Another State? Or do I skip this and claim in NJ for NY? I take it it must be one state being credited for another not doing it for both... 

Last few years I have always received a refund... And last year the only difference was the midyear move.

Using TurboTax Online.

[TomD8]

The "other state credit" is granted by the state of residence.  NY will credit you for the taxes paid to NJ during the portion of the year that you were an NY resident.  NJ will credit you for the taxes paid to NY during the portion of the year that you were an NJ resident.

After your move to NJ, your income will continue to be taxable by NY (as well as by NJ) if you worked remotely from the NJ location for your own convenience, rather than because you were assigned to or required to work in NJ by your employer.  This is known as the "Convenience of the Employer" rule.  Details here:

https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf

NJ's tax rules for non-residents and part-year residents are detailed in this NJ tax publication:

https://www.nj.gov/treasury/taxation/pdf/pubs/tgi-ee/git6.pdf

Here are TT's instructions on filing part-year resident state returns:

How do I file a part-year state return? (intuit.com)