When the case was argued last month, Judge Katzmann said that he did not expect his court to have the last word. “This case seems bound for the Supreme Court,” he said.

Mr. Vance’s office has agreed to put off enforcing the subpoena so long as Mr. Trump’s lawyers seek Supreme Court review within 10 days of the appeals court’s decision and ask the justices for prompt action, which the lawyers have said they will do.

The Supreme Court is dominated by five Republican appointees, two of them named by Mr. Trump. But earlier Supreme Court cases in which presidents sought to avoid providing evidence did not break along partisan lines.

The court was unanimous in ruling against Presidents Richard M. Nixon and Bill Clinton in such cases, with Nixon and Clinton appointees voting against the presidents who had placed them on the court. The Nixon case led to his resignation in the face of mounting calls for his impeachment. The Clinton case led to Mr. Clinton’s impeachment, though he survived a Senate vote on his removal.

Read together, the two decisions — United States v. Nixon in 1974 and Clinton v. Jones in 1997 — suggest that Mr. Trump will face an uphill fight in winning his argument that he is entitled to complete immunity from criminal process of any kind so long as he is in office, said David A. Strauss, a law professor at the University of Chicago.

“U.S. v. Nixon established that documents reflecting the most sensitive presidential discussions can be subpoenaed,” Professor Strauss said. “The documents in this case have nothing to do with government business. Clinton v. Jones established that the president has to respond to an ordinary civil suit, even by giving personal testimony. Here we’re not talking about personal testimony or anything the president has to do personally.”

Mr. Trump’s lawyers have said that their case is different, calling the subpoena “a bad-faith effort to harass the president by obtaining and exposing his confidential financial information, not a legitimate attempt to enforce New York law.”