You didn't say what's on IT-203 line 62. Since line 66 is the total of lines 60 through 65, in order to figure out where the additional withholding came from, we first have to determine whether it came from line 62 or from one of the other lines that are included in the total. If line 62 is not $3,740, what is on the other lines, 60 through 65? Please post what's on those lines, and ignore the rest of this reply.
If line 62 is $3,740, save a PDF of your tax return with all the government and TurboTax worksheets included. (See the link below for instructions.) In the New York return there will be a Tax Payments Worksheet. (There is also a Tax Payments Worksheet in the federal return, and there might also be one for your resident state, since you apparently do not live in New York. Make sure you are looking at the Tax Payments Worksheet for New York.) On the New York Tax Payments Worksheet, line 14 should be $3,740. That's where the $3,740 on IT-203 line 62 comes from. What is on each of the lines 9 through 13 above that?
If line 9 of the New York Tax Payments Worksheet is $3,740, and there is nothing on lines 10 through 13, then the $3,740 came from a W-2, or from more than one W-2. Look at the Form IT-2 summary of your W-2 forms. (There can be two W-2s on Form IT-2, and there might be more than one IT-2.) That will show you all the W-2 forms that were entered, and, in box 17a, the amount of New York state tax that was withheld on each one. See if there is more than one W-2 with $1,870 in box 17a. The IT-2 forms show you what was entered in TurboTax, which might be different from what is on the W-2 form from your employer.
How do I save my 2022 TurboTax Online return as a PDF?
