Box 14 letter H is an adjustment for section 1411 and letter I is section 199A information. Honestly I don't have any idea what would apply to NY for either of those numbers. But New York taxes earnings from non residents so the really important numbers on your K1 for New York tax purposes are in boxes 1 thru 11.
In TurboTax you should be able to enter the K1 into your federal return and have it carry over to the state returns from there.
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