A few children among the refugees belong to families involved in the drug trade, and rival gang members have threatened them, bringing the specter of gangland killings to the high school, law enforcement and school officials say.

“Some of the families who are fleeing from Mexico are doing it because they were somehow participating in these acts,” said Jose G. Franco, the school superintendent, “and if you want to get at somebody, you get at their children.”

The Hudspeth County Sheriff’s Department and the state police are keeping a close eye on unknown vehicles parked near the schools. The school district has for the first time hired a law enforcement officer to patrol its three campuses and has installed security cameras. Spectators are now barred from football and basketball practices.

“The kids are a little bit on edge, you know,” said Constable Jose Sierra, who patrols the schools. “When we see a different car, we start to get phone calls.”

Not everyone coming from El Porvenir is seeking asylum. Many Mexicans in towns along the river have special border-crossing cards, which let them cross for up to 30 days to do business and shop near the border. But some have used the visas to relocate their families temporarily to Fort Hancock and other small towns on the Texas side.

Those who have temporary tourist visas or who can obtain business visas because they have enough money to start businesses in the United States are also moving their families across the border. (Cities like El Paso and San Antonio have had real estate booms and a flourishing of small businesses and Mexican restaurants as a result.)

Image The gate at the border. Credit... Ivan Pierre Aguirre for The New York Times

Other Mexicans who were once happy living in Mexico are taking advantage of whatever means they have to obtain a visa and get out. Some were born in a hospital on the United States side and are American citizens, for instance, or have married citizens but have never applied for residency.