"In Clinton v Jones, the United States Supreme Court held that separation of powers concerns did not preclude a federal lawsuit against a sitting President of the United States..."

"... based on unofficial acts allegedly committed by him before he assumed office. The Court expressly cautioned in that decision that different concerns, including the Supremacy Clause of the United States Constitution, might influence the result if such a case were brought against the President in state court. However, the Court did not rule that such a suit could or could not proceed. This matter gives us an opportunity to squarely address the question.... [S]ubjecting the President to a state trial court's jurisdiction imposes upon him a degree of control by the State of New York that interferes with his ability to carry out his constitutional duty of executing the laws of the United States. Since the Supremacy Clause guarantees that any effort by the individual states to annul, minimize, or otherwise interfere with those laws will be struck down, it follows that any effort by a state court to control the President must likewise fail.... Plaintiff sees no functional difference between the effect a federal court's supervision of litigation would have over a President's executive power and the effect a state court's would... Defendant argues that the Supremacy Clause acts as an absolute bar to state courts' authority to exercise jurisdiction over a sitting President, citing McCulloch v Maryland... which held that 'the states have no power, by taxation or otherwise, to retard, impede, burden, or in any manner control, the operations of the constitutional laws enacted by congress to carry into execution the powers vested in the general government.'... [T]he President should not be forced to defend this lawsuit while he is in office. Therefore, in my view the action should be stayed until such time as defendant no longer occupies the office of President of the United States."

Writes Justice Mazzarelli, dissenting in Summer Zervos v. Donald J. Trump, in which one of the intermediate appellate courts in NY held that a defamation case against a President of the United States can go forward in state court. The case isn't based on the President's official actions as President, so the President's absolute immunity does not apply. It's like Clinton v. Jones, where the President is sued for actions outside of his official duties as President of the United States, but different from Clinton v. Jones, in that the case isn't in federal court.