Zabi-Ullah Hemmat wasn’t just one of 415,816 illegal immigrants caught at the southwest border in fiscal 2016. Nor was he just another of the 84 people from Afghanistan apprehended by Border Patrol agents that year.

What made Mr. Hemmat of special interest to authorities is that when he was snared by agents after 11 p.m. on a chilly November night and they ran his name through federal databases, he came back listed on the no-fly terrorist watch-list.

Mr. Hemmat is one of the terrorism suspects caught trying to sneak into the U.S. from Mexico — a category of people that is very much part of the current debate over illegal immigration, with President Trump insisting his border wall would deter people from being able to reach American soil and Democrats saying there’s no real danger.

Mr. Hemmat’s case suggests both may be wrong.

He was indeed on U.S. terrorism lists, linked to both the Taliban and a plot somewhere in North America, according to Department of Homeland Security documents. But after he was caught, wandering in southern Arizona with two Mexican guides and five other men from Afghanistan and Pakistan, he said he had sneaked in by crawling under an existing border fence near Nogales, Arizona.

Democrats say the number of potential terrorists who do try to enter via the land border is negligible, and several news reports over the last week say the numbers amount to the low double digits each year.

Homeland Security Secretary Kirstjen Nielsen says the exact numbers are too sensitive to release, but she says it’s on the increase.

Homeland Security does say it “encountered” more than 3,000 “special interest” migrants — people whose nationalities and travel patterns made them potential national security concerns — at the southern border in 2018.

“I am sure all Americans would agree that one terrorist reaching our borders is one too many. These are just the terror suspects we know about who reach our border,” Ms. Nielsen said on Twitter, defending the White House’s claims.

The Washington Times has not been able to independently verify a total number of terrorists who have entered via the southwest border, but it has spent several years tracking cases such as Mr. Hemmat‘s, where someone with terrorist connections was nabbed after sneaking in.

Among those were four Turkish men who claimed ties to a Marxist insurgency known by the acronym DHKP/C, who paid $8,000 apiece to be smuggled into the U.S. They traveled from Istanbul via Paris to Mexico City, then shuttled to the border where they were caught in 2014.

Analysts at the time said the men’s arrival exposed the existence of networks capable of smuggling potential terrorists into the U.S.

The worries were big enough that the government created Operation Citadel, a joint program with Homeland Security, the Pentagon and international partners intended to try to clamp down on those smuggling networks.

One of the big successes of Operation Citadel was sniffing out Sharafat Khan, who ran a network that smuggled people from Pakistan, Afghanistan and Bangladesh from Asia to Brazil then up the spine of South and Central America, through Mexico to the U.S. border.

Court documents show U.S. Immigration and Customs Enforcement nabbed upwards of 100 people from 2014 to 2016 who identified being smuggled by Khan. In some cases, the migrants were flagged en route by American partners in countries such as Panama and Colombia. Other times, they managed to reach the U.S. border before being detected.

Four of those, including Mr. Hemmat, popped up on U.S. terrorist watch lists. ICE acknowledged those in a statement last month, upon Khan’s deportation, obliquely noting that “several of the individuals smuggled by Khan’s organization had suspected ties to terrorist organizations.”

It’s not known how many others Khan smuggled managed to evade detection, nor whether any of those were on terrorism lists.

Smuggling network leads long trip to border

Khan, a Pakistani who also went by the alias “Dr. Nakib,” lived in Brasilia, where he oversaw recruiters who found clients in Central Asia and operators who would shepherd the migrants on the journey, arranging transportation and food and lodging.

Mr. Hemmat flew through Dubai to Brazil, then began a trip that lasted months, through Peru, Ecuador, Colombia, Panama, Costa Rica, Nicaragua, Honduras, Guatemala and Mexico. Along the way, Khan’s clients were forced on a 100-mile walk through the Darien Gap, a tropical forest in Panama that cannot be crossed by vehicle. The foot journey can take up to 10 days.

Court documents don’t say how much Mr. Hemmat paid, but Khan’s going rate ranged from $3,000 to $15,000, authorities said in court papers.

During the trip, Mr. Hemmat was detected transiting Panama, where officials took his fingerprints as part of Operation Citadel. They alerted U.S. officials but released him and he continued on his journey. The documents seen by The Times do not give a reason for his release.

Finally at the U.S.-Mexico border in November 2015, he met up with five other men, one from Afghanistan and four from Pakistan, and two Mexicans who were to serve as foot guides.

One was a repeat smuggler, having done prison time for a past conviction. The other was an illegal immigrant who had been deported from the U.S. but was determined to get back to Tucson, Arizona, to the construction site where he had been working as a mason. That man received a $2,000 discount on the $3,000 crossing fee in exchange for serving as a guide.

They crawled through a hole underneath an outdated section of border wall near Nogales in broad daylight — and then immediately got lost, wandering for three days and three nights, with temperatures dipping near freezing at night. They didn’t have heavy clothing and quickly ran out of food and water.

It didn’t help that the Mexicans only spoke Spanish, while the clients spoke their native tongues, and one, Mr. Hemmat, also spoke some English — though neither of the foot guides did.

Things got testy along the way, with the clients saying the foot guides got “aggressive” with them when they complained about the bungled arrangements.

Near midnight on the third day, they were detected by a Border Patrol surveillance unit and agents swooped in, nabbing them near Patagonia, about 15 miles north of the boundary line.

Hemmat, others flagged on no-fly list

The exact nature of Mr. Hemmat’s terrorist dealings remains murky, though documents say he was listed among the more than 80,000 names on the no-fly list as of 2016.

A border alert said Mr. Hemmat had been flagged for past involvement in a plot to conduct an attack in the western hemisphere, either in Canada or the U.S. No more details were provided in the secret document viewed by The Times. Mr. Hemmat also had family ties to members of the Taliban, the border alert said.

Mr. Hemmat told agents he was a doctor and performed vaccinations in Afghanistan. He and the five men with him all intended to lodge asylum claims, according to court documents. It appears those claims failed, and he was to be deported.

It’s not clear what finally happened, though there is no record of a criminal case against Mr. Hemmat. ICE didn’t respond to inquiries about Mr. Hemmat.

Just months before Mr. Hemmat and his group were caught, Border Patrol agents in Arizona nabbed two other men from Pakistan who were flagged for terrorist ties. The documentation seen by The Times showed one was on the watch-list as an associate of a known or suspected terrorist. The other was not watch-listed but did have “derogatory information” in the system, where he was also identified as an associate of a known or suspected terrorist.

They, too, were smuggled by Khan, as was another Pakistani man detained in Panama during his trip north with two others. When Panamanian authorities ran his identity, they found him on a U.S. terrorism watch-list.

Authorities say Khan maintained safe houses and paid people in each country along the route, selling his services to anyone willing to pay.

Authorities sniffed him out in late 2014 and began working with international partners to probe his activities and to keep track of those he was smuggling.

Brazil served a search warrant on Khan in the spring of 2016, and he fled, making a run for Pakistan. He was snared during a layover in Doha in June 2016 and extradited to the U.S.

After a lengthy legal battle, Khan was convicted and sentenced to 31 months in prison.

“Sharafat Khan organized an intricate network that was open to the highest bidder to transport undocumented migrants, regardless of who they were, from Pakistan and elsewhere through Brazil and Central America and then into the United States,” Angel M. Melendez, special agent in charge at ICE’s Homeland Security Investigations office in New York said at the time of Khan’s sentencing.

The judge who sentenced him was more direct about the risks.

“You don’t know whether they’re seeking a better life or whether they’re trying to get in here to engage in terrorism,” Judge Reggie B. Walton told Khan at his sentencing. “Just because you had good intentions doesn’t mean the people you were helping have good intentions. People could have died, people could have gotten injured, families could have lost loved ones.”