The $500 "Other dependent" credit phases out at $200,000 of modified adjusted gross income ($400,000 for married couples filing jointly) compared to the old exemption phase out at $261,500 ($313,800 for married couples filing jointly).
How does he claim it? First you do not show him as a dependent on your return. Using Turbotax, he first answers that somebody CAN claim him as a dependent. Then he answers that nobody will actually claim him. That will allow him to claim the nonrefundable tuition credit
