My NY State return was accepted at the amount of1243.00 and they deposited 551.00 into my account. Why is this?

The state could have made a change to your return that has impacted your refund, or they could need more information to finish processing part of your refund. Another possibility is that it was partly taken in order to offset a prior debt owed.

In all of the situations above, you will receive a letter explaining exactly what happened, what additional information they might need (if any) and contact information. You could also call your state tax department before receiving this letter, they might be able to access your account and explain what happened. 

Here is the contact information for New York State Dept. of Taxation and Finance: 

https://www.tax.ny.gov/help/contact/default.htm

Your refund amount may differ from what you claimed on your return if:

• we were able to refund part of the amount you claimed, but need more information to process the rest (within 30 days, we will send you a letter explaining what we need from you); or
• your tax return had one or more errors. If we:
• sent you a paper check, we will also send you Form DTF-160, Account Adjustment Notice. For an explanation of any errors on your tax return, see Section A, Explanation of adjustment.
• directly deposited your refund, within 30 days we will send you Form DTF-160, Account Adjustment Notice. For an explanation of any errors on your tax return, see Section A, Explanation of adjustment.

https://www.tax.ny.gov/pit/file/more_info_refunds.htm