“But with the passing of the day of lands so cheap as to be well-nigh free, we are coming to confront a new set of conditions. It has been found necessary to inquire whether under these new conditions we can be sure of finding employment for the diverse elements and enormous numbers of new immigrants that are offered to us. We are all agreed, whether we be Americans of the first or of the seventh generation on this soil, that it is not desirable to receive more immigrants than can reasonably be assured of bettering their condition by coming here. For the sake both of those who would come and more especially of those already here, it has been thought wise to avoid the danger of increasing our numbers too fast. It is not a reflection on any race or creed. We might not be able to support them if their numbers were too great. In such event, the first sufferers would be the most recent immigrants, unaccustomed to our life and language and industrial methods. We want to keep wages and living conditions good for everyone who is now here or who may come here.”

Seton Hall Address (2002)
Context: They killed in the name of God. But they are not the first. This began in pre-history; the tragedy is that it persists today.
Some would characterize the events of 9-11 as a clash of civilizations, and a conflict of religions. And to many it seems a simple and satisfying explanation.
But others would suggest, correctly in my view, that such an interpretation is both wrong-headed and dangerous. They recognize a civil war within Islam itself, as contending factions compete for power. They would argue that we must influence the struggle where we can, by supporting greater attention to the secular structures in the Islamic world, and by encouraging our own American Islamic community to speak out in support of America’s democratic values.
Ultimately, your generation will have the decisive voice. You will determine whether rage or reason guides the United States in the struggle to come. You will choose whether we are known for revenge or compassion. You will choose whether we, too, will kill in the name of God, or whether in His Name, we can find a higher civilization and a better means of settling our differences.
And this is not a new choice, not for your generation — it is a choice that many others have faced throughout history. Only now, we can hope that with your help and engagement we can find a new answer.

This misattribution seems to have originated as improper quoting of an actually site-created preamble to an online page of Jefferson's quotes or paraphrases at the site Family Guardian https://famguardian.org/index.htm — self described as a "Nonprofit Christian religious ministry dedicated to protecting people and families from extortion, persecution, exploitation, socialism, divorce, crime, and sin." Among the preambles to their pages, these remarks summarizing the site creators' assessments on "Immigration Policy" https://famguardian.org/subjects/politics/thomasjefferson/jeff1280.htm for their page of Jefferson's statements regarding the subject, have occasionally been wrongly copied and distributed in various internet articles and comments as if they were direct "quotes" of Jefferson, sometimes with spurious citations to specific documents, most commonly the source of the first actual quote citation on that page: an 1806 letter to Albert Gallatin. It should also be noted that even the provided "quotes" at this site are not absolutely reliable, as on their index page for quotes of Thomas Jefferson on Politics & Government https://famguardian.org/subjects/politics/thomasjefferson/jeffcont.htm they indicate that some of the "quotes" they use are modernized and "generalized" (or in other words: paraphrased) in ways which diverge slightly from literal quotations of the original sources cited.
Misattributed

We Will Not Be Terrorized (December 2015), Naturalization Ceremony speech (December 2015)

17 September 2015 according to 18 September 2015 article by Peter Edwards mentioning "the phrase “old stock Canadians” used by Prime Minister Stephen Harper in Thursday’s leadership debate." https://www.thestar.com/news/canada/2015/09/18/old-stock-canadians-phrase-chills-prof-ignites-twitter.html
2015

James Martin (1978) The wired society. p. 3

1962, Rice University speech
Context: We set sail on this new sea because there is new knowledge to be gained, and new rights to be won, and they must be won and used for the progress of all people. For space science, like nuclear science and all technology, has no conscience of its own. Whether it will become a force for good or ill depends on man, and only if the United States occupies a position of pre-eminence can we help decide whether this new ocean will be a sea of peace or a new terrifying theater of war. I do not say that we should or will go unprotected against the hostile misuse of space any more than we go unprotected against the hostile use of land or sea, but I do say that space can be explored and mastered without feeding the fires of war, without repeating the mistakes that man has made in extending his writ around this globe of ours.

1920s, The Genius of America (1924)

Founding Address (1876)