My Form W-2 shows State Withholding equal to my State Wages because I did not take any payment from this side job and had all my wages paid to my resident State because I always owe taxes in my resident state because my major job is in another state. Turbo Tax says I can't efile if a W-2 has state withholding greater than 50% of state wages. Fine. But NY State (which I need to efile), will not accept mail in returns, and I can't efile NY without efiling Federal. So now I can't file any of my returns because Turbo Tax will not accept that my W-2 is correct. It is not against the tax code to have state withholding greater than 50% of state wages.
You are required to e-file your NY return IF "your software supports the electronic filing of your return." In your situation TurboTax does not support electronic filing of your NY return. Therefore you are not required to e-file your NY return. You can file it by mail. New York does accept mailed tax returns.
You can mail your New York return. Just attach an explanation as to why you are mailing it. The only work-around I can come up with is to leave the state tax withholding for New York blank on the W-2 entry. Instead, enter the amount of New York tax withheld as an estimated tax payment. It's not ideal and it could create issues with New York, but it would allow you to e-file your federal return and other state return(s).