My case is unique as described follows. I did not work or stay or did not related through other way for a single day to NY state for year 2011. For whole year 2011, I earned and worked in NJ state only. I worked in NY for whole year of 2010 and my last payslip of year 2010 (last 2 weeks of Dec 2010) was generated on 1st week of Jan 2011 with income from last 2 weeks of Dec 2010 and tax withheld for NY state. That income is reported to my 2011 W2. Please help me how to report that income and tax withheld while filing NY state return for 2011.

Even though you didn't work in NY in 2011, you were paid in 2011 for work performed in NY and hence have to pay income tax to NY State for NY-source income. File as non-resident (form IT-203). Then when you do your NJ oncome tax take the credit for taxes paid to other jurisdictions (namely NY) so that NJ doesn't tax the same income.