It depends, the amounts may be reported on your W-2. In the states section in boxes 15-17, your wages may already be allocated between NJ and CA. If they are not, you will have to calculate the allocation yourself.
When it comes to allocating your earnings between California and New Jersey, the most accurate way is to look up your old pay stubs and see how much you had earned prior to the move. That income gets allocated to New Jersey, the remainder gets allocated to California.
If you do not have access to your old pay stubs, you may allocate based on the number of days you were a resident in each state. This really only works if your income was earned more or less evenly throughout the year.
You will handle the allocations in your NJ and CA returns. It does not have to be accurate down to the dollar, just make sure you are allocating the entire amount to one state or the other.
In the My Info section of your return, enter your state of residence as California. Select Yes / New Jersey to I lived in another state in 2021. Enter the date that you became a resident of California.
On the next screen, under Other state income, make sure New York is selected. After completing your federal return, complete your New York nonresident return next. This is so that NJ and CA may properly apply a tax credit for the taxes paid to NY.
With regards to your earlier question, the reason both CA and NY taxes are being withheld is that you are being taxed by your nonresident state of NY and your resident state of CA. CA gives you a credit for the taxes you pay to NY, but since CA taxes are so high, they withhold an additional amount above what NY is withholding.
