the ratification and implementation of the Constitution (1789), one of the Founding Fathers voted for Alien and Sedition Acts (1798) which authorized the president to deport non-citizens, defined as "Aliens" during wartime.
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That would indicate to me that regardless of whether it is theoretically possible to have federal control over citizenship while having no authority over immigration that at least one of the Founding Fathers felt that they had given authority over immigration to the federal government in the constitution.