Assume that the most recent W-2 is correct, and proceed from there.
If it shows you paid California tax, you will need to file a Non-Resident CA State Return to report that. The W-2 should show the Amount of CA Income that applies to the CA Tax Paid in Boxes 15-17. That's all you report on the CA return.
Don't think in terms of 'paychecks', but 'total income earned' in that State. You'll file a Resident State Return for New York, reporting the total income you earned while living there, and the total NY Tax Paid, as shown on your W-2.
You'll also report that you paid $X CA Tax. NY will give you credit for tax paid to another state on income earned while living in NY, so you are not double-taxed. As far as your employer owning you money for the difference in CA tax and NY tax, you would need to take that up with them.
Since they withheld tax for the wrong state initially, you are dealing with it at tax time, but don't worry, it will all work out.
Be sure to prepare your non-resident California return first.
@missjq885
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