Final answer:
The question seems to contain a mistake as none of the listed options (Thomas Jefferson, John Adams, John Quincy Adams, or John Jay) are noted as having taught constitutional law at Yale in between presidential and chief justice roles.
Step-by-step explanation:
The individual who taught constitutional law at Yale in between being president and chief justice is not explicitly mentioned in the materials provided. However, we can infer from the context that none of the options provided (Thomas Jefferson, John Adams, John Quincy Adams, or John Jay) fit this description, as John Jay was the first chief justice who resigned to become governor of New York and John Adams was the second president who later appointed John Marshall as Chief Justice. Moreover, there is no mention of any of them teaching at Yale after serving as president and before serving as chief justice. Thus, both the question and the options appear to contain an error or are referring to an individual not listed.