What taxes I have to pay in MA statewhere I live since last year, if I getting SSA pension and New york City teacher retiremnt system pension?

MA does not tax Social Security Benefits.  Also, MA allows a reciprocal deduction of pension income for NY public retirement distributions.  Since NY law states NY would allow a deduction of up to $20,000 for taxpayers age 59.5 or older who receive pension distributions from another state's public retirement system, then MA will do the same for MA taxpayers receiving a NY public retirement. 

Here is the MA reference. 

If you are younger than 59.5 and/or your NY pension is over $20,000 then you can contact you pension plan administrator to have MA taxes withheld going forward.  The MA withholding amounts will show on form 1099R in box 14 with MA in box 15.  

If you are eligible for the MA deduction (age 59.5 or older) below are the steps to get the deduction on your MA returns.

1. Wages & Income
2. Retirement, Social Security
3. Form 1099R
4. Enter form 1099R information
5. "Where is the Distribution from?"  Select "None of the above"
6. Qualified Plan
7. Continue to complete the 1099R entry
8. In the MA state interview
9. Update the "Adjustments" section
10. Edit the 1099R payer line
11. Select "No" Not excluded
12. Done
13. The "non-taxable MA pension" box should be blank/empty
14. Continue to the page "Qualified Contributory Pension"
15. Answer "Yes"
16. Enter your pension distribution amount up to "$20,000"
17. Continue