Although the title of this article--Shouting Stephen Miller Melts Down on Fox News Over Deported Dad--uses some loaded language (with "meltdown" having a strong connotation), I would argue that this claim is true.
Whether or not Stephen Miller's conduct in the Fox News interview meets one's expectations of "melting down" may constitute a gray area, but what I saw in the video was a news reporter ranting about a story, repeatedly cutting off interjections by the in-studio anchor, referring to the in-studio anchor by first name several times, and seemingly improvising and yelling quotes such as, "his [the deported individual's] only options in life, Bill, his only options in life, are to be deported to El Salvador, or to be deported to some other country. That's it. He has a deportation order. So Bill, you tell me, what country should we deport him to? Tell me, please. Please, tell me." This dialogue begins at the 3:01 mark of the video, linked with the article below. I would consider this heated, inappropriate and unprofessional on-air behavior, and thus I would accept the article's claim that this was a "meltdown" on Fox News.
Shouting Stephen Miller Melts Down at Fox News Host Over Deported Dad
Of course, this does not validate the truthfulness of anything that Stephen Miller says during the interview. This only asserts that he did indeed "meltdown" on television. For the purposes of fact-checking the original claim, then, it is true that a reporter named Stephen Miller had a shouting "meltdown" on Fox News. To verify that this report really comes from Fox News, I found the clip uploaded by Fox News's YouTube account: Trump official goes off on false narrative about deportation case: 'ALL A HOAX' - YouTube This affirms that this "meltdown" occurred on Fox News.
Finally, to verify that the "meltdown" occurs over a deported father, this article from BBC--a trustworthy news source--goes into more context about the situation, and affirms that the individual to which Steven Miller refers, Kilmer Abrego Garcia, has not only been deported but also has three children. Kilmar Abrego Garcia and MS-13: What is alleged and what we know This rounds out the entire claim of the article as true.
For the sake of investigating the original source of this claim, The Daily Beast, I used Media Bias/Fact Check.com to check the typical quality of their reporting. Media Bias/Fact Check.com claims that The Daily Beast is a left-leaning news source with a "mixed" level of factual reporting due to use of loaded words, which we have already established ("meltdown"). Daily Beast - Bias and Credibility - Media Bias/Fact Check This means that when generally using this source, readers should be wary of attempts to unfairly defame competing Conservative media, such as Fox News and its affiliated reporters. However, in this case, the claim that "Shouting Stephen Miller Melts Down on Fox News Over Deported Dad" is true; one can determine this because The Daily Beast made the "tracing" step of fact-checking simple by embedding the primary source of the claim in their article so viewers can see the video for themselves.
To provide one last piece of evidence affirming the validity of this claim, a quick YouTube search of "Stephen Miller" populated videos about him with titles including phrasing such as "Stephen Miller Issues Brutal Takedown of Kamala Harris," "Stephen Miller Throws Down the Hammer on Biden," and "Stephen Miller: Sucking the Blood Out of American Democracy" from Forbes Breaking News, Fox News and The Daily Show (a politically diverse selection of accounts), respectively.
Stephen Miller Issues Brutal Takedown Of Kamala Harris After Her San Francisco Speech Blasting Trump
Stephen Miller throws down the hammer on Biden for the catastrophes Trump has had to reverse #news
Stephen Miller: Sucking the Blood Out of American Democracy | The Daily Show - YouTube
In other words, Conservatives and Liberals both agree that Stephen Miller is known for this intense speaking dynamic, so despite The Daily Beast's bias, it is true that Stephen Miller conducted himself on-air in the manner that the title of the article claims.