The papers each bore two names, one unknown, the other ubiquitous, facing off across the letter V. The V was important. It meant that in America, anyone could sue the president of the United States and hope to win.

In New York, there was Darweesh v. Trump. In Colorado, Hagig v. Trump. There was also Ali v. Trump, Zadeh v. Trump, Bayani v. Trump, Albaldawi v. Trump.

This was the same America whose president had tried to fence out the Darweeshes and the Zadehs of the world, declaring a ban on travelers from predominantly Muslim countries that trapped people in airports and interrupted lives. And the same America where an Ali or a Hagig could do what, back home, would have been the unthinkable: call a lawyer; stop the president.

“It was never my intention to go against the president of the United States,” said Mohamed Iye, a Somali-born American citizen whose Somali wife and two American daughters were stranded in Nairobi after President Trump’s first travel order prevented them from joining him in Minnesota. “I was just following the law and doing everything the way it’s in the books. And it came to this.”

It came to this: more than 50 lawsuits across the country, with at least as many individual plaintiffs; a reprieve from a federal judge in Seattle; a new ban; and, on March 15, l, a new set of roadblocks from federal judges in Hawaii and Maryland. The government is opposing those decisions, which have drawn Mr. Trump’s fury. His administration has insisted it will prevail.

The people who sued the president this winter were Muslim, and they were Christian. They were professors and grocery clerks. They were parents, daughters and sons-in-law, and they were married but divided or just planning the wedding. They were Americans, or trying to become ones.

They sued to place a different bet on the Constitution, staking their names on lawsuits that were part legal theory, part prayer.

The ban “isn’t really what this country’s about,” Mr. Iye, 66, said recently through an interpreter. “I wouldn’t have brought my family if I didn’t love this country, if I didn’t believe this country was the land of dreams.”

Mr. Trump’s original executive order, signed on Jan. 27, barred visitors from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen, including those with valid visas, from coming to the United States while federal agencies tightened their vetting procedures. It also blocked the entry of all refugees worldwide. The revision this month, an attempt to satisfy the courts, removed Iraqis, green card holders and visa holders from the list.

If the plaintiffs in many landmark constitutional tests are meticulously chosen for their compelling personal stories — think Jim Obergefell, of Obergefell v. Hodges, which established a national right to same-sex marriage — the first travel ban plaintiffs emerged out of frantic necessity, plucked from airports where they had been denied admission or from cities nationwide where citizens were waiting to reunite with relatives.

There was Allan Hakky, an Iraqi Kurd who found himself picking up the phone and volunteering to join a lawsuit after his mother-in-law had to abandon plans to visit a daughter with a premature baby in the United States.

“I’m a very private person, so to actually have my name on a federal lawsuit, on something so polarizing and so in the headlines — if somebody told me this a year ago, I’d probably laugh at them,” said Mr. Hakky, a technology executive who has lived in the United States for 27 years. He said strangers had harassed his home with threatening calls ever since the lawsuit became public.

But, he added: “I don’t want to have to wake up one day and find a bunch of military people outside my house taking me to a camp the way they did to the Japanese. It’s one of those things that, if you don’t fight it at the beginning, does it get worse?”

There was Juweiya Abdiaziz Ali, 23, a home health aide near Seattle who was within a month or two of bringing her 7-year-old son to live with her when the first executive order was issued. When the Northwest Immigrant Rights Project, a nonprofit in Washington State, told her about efforts to sue, she offered to help.

“I hope that everybody understands this isn’t just something on a piece of paper,” Ms. Ali, a Somali-born naturalized citizen, said. Even if the legal challenge does not succeed, she said, “I can go to sleep at night knowing that I have done what I can legally to have my son with me.”

And in Euless, Tex., there was Paul Harrison, 61, American born and raised, whose engagement to an Iranian man the ban threatened to put asunder. The visa application of Mr. Harrison’s fiancé, whom he met on vacation, had been approved only 10 days before the first order took effect.

Stranded 7,000 miles apart, he emailed every civil liberties group he could think of without expecting a response, “because we feel like we’re just tiny little fish in a great big pond,” said Mr. Harrison, who trains new flight attendants for American Airlines. He had never been one for politics before, he said.

The American Civil Liberties Union asked him to sign on to the lawsuit it had filed in Maryland, International Refugee Assistance Project v. Trump. This month, it became one of the two cases in which federal judges blocked the revised ban from taking effect.

Like the other plaintiffs, the couple veer between dread and hope with each successive legal victory, each sign that the Trump administration will not relent.

“We look at each other and we say, ‘Gosh, we don’t know whether we should laugh or cry at any given moment,’” Mr. Harrison said from Istanbul, where, unlike in Tehran, the couple is free to act like one. “Should we be happy? Should we be scared?”

Still, in an ordeal defined as much by the minutiae of plane tickets and visa applications as by the sweep of headlines and history books, the fundamentals are never far from view.

In Iran, “there is no freedom of speech, no freedom of press,” said Ali Asaei, 27, an Iranian who earned a master’s degree from the State University of New York at New Paltz and now works at a psychiatric research institute in Manhattan. “One of the reasons I came here was because I thought, here we’re going to have the freedom of speech and religion and all these. But if I don’t have those freedoms, then what would be the point of staying here?”

Mr. Asaei, a plaintiff in Pars Equality Center v. Trump, has not seen his family in four years. Their applications for visas to visit him were rejected after the initial travel ban. He plans either to return to Iran or to find another country where he might be more welcome.

Since filing the lawsuit known as Hagig v. Trump, Zakaria Hagig, 24, a business student from Libya at the Community College of Denver, has found himself in a split-screen America, being cheered by a crowd of protesters one moment, recoiling from hostile Facebook messages the next.

Not that the plaintiffs have needed to sign court papers to feel the tremors of what many Muslims say is a heightened Islamophobia.

In Los Banos, Calif., Ahmed Mohammed Ahmed Ali, 39, a grocery store clerk born in Yemen and naturalized in 2010, has been able to bring his 12-year-old daughter to California after the first executive order stranded them in Djibouti for a week. It is a relief, he said, to be done with the incessant attention from the news media.

His daughter, now a citizen, is settling into the sixth grade. Mr. Ali, however, is still on edge over a threat no court can banish.

“It’s started to feel a little bit different — everybody watching you, everybody looking at you. Something you never had it before, you never feel it before. Racist words,” he said. “If I take my kids and wife to go shopping, to do this, to do that, I always worry that somebody will stop me on the way.”

The plaintiffs’ faith has been shaken, strengthened and stretched again. So far, the America they know has come out on top.

“In a funny way, even though I’m discouraged about how they’re vilifying Muslims and using the presidential seal of approval to vilify Muslims, the lawsuits and people’s response has made me feel even stronger about this country,” Mr. Hakky, the technology executive, said. “In any other country, when the president wants something, he gets it. The fact that a lowly judge somewhere can basically stop the most powerful man on Earth with a simple ruling is gratifying, and it shows what this country’s all about.”

His mother-in-law visited recently. Mr. Harrison and his fiancé are still awaiting a visa. Ms. Ali video chats with her son regularly, struggling to explain their separation.

And in February, Mr. Iye embraced his wife and daughters in the arrivals hall of Minneapolis-St. Paul International Airport — reunited, after more than two years apart, because of and in spite of the United States of America.