In USA there is this concept or "rule of law" that includes the principle that no one is above the law.
About this the book "A Companion to the US Constitution and Its Amendments" (by John R. Vile) says on page 80
...American officers, like the president himself, pledge first and foremost to uphold the Constitution of the United States. In this way, they affirm that the rule of law is superior to the rule of a human leader.
Now there is this case, as reported by NBC, where the New York State Supreme Court Justice has ordered the president to answer questions under oath for a civil suit in the Bronx involving his security guards.
Considering a situation where the president would not provide any answer to the questions, or provided some flippant answer, would the judge have the authority to throw the president in jail for contempt of court?