HOUSTON — When Texas authorities began charging migrants who crossed into the state from Mexico with trespassing last year, officials quickly encountered a problem: The two small rural counties tasked with prosecuting the cases became overwhelmed.

Among the many issues — crowded jails, a lack of defense lawyers — there were not enough judges, particularly in Kinney County, a border community about 120 miles west of San Antonio where the state’s effort has been most aggressively enforced. Three retired judges were brought in by the state to help, starting in the late summer.

Then, last month, the county attorney accused the judges of impropriety. The next day, all three were replaced with others handpicked by the top county official, Tully Shahan.

The shake-up surprised the judges and outraged lawyers for the migrants, hundreds of whom remain jailed and awaiting prosecution. Immigration advocates accused Mr. Shahan of supplanting judges who did not rule as he wanted in a county eager to use local law enforcement to turn back what officials have called an “invasion of illegal aliens.”

The program, created last year by Gov. Greg Abbott and known as Operation Lone Star, authorized state and local police departments to partner with the owners of borderland ranches and use trespassing laws to arrest migrants who cross their land. Just two of the state’s 32 border counties — Kinney and its neighbor to the west, Val Verde — have adopted the approach.

More than 2,500 migrants have been arrested on trespassing charges, all of them men. (Under the Texas program, women and children found on private land are handed directly to immigration officials.) About 900 are still being held in state prisons.

The misdemeanor trespassing arrests, contentious from the start, have come under increased scrutiny in recent weeks.

This month, a state court judge dismissed the case of a migrant arrested on trespassing charges in Kinney County after his lawyers argued that the arrest violated the U.S. Constitution because only the federal government has jurisdiction over immigration law. The county has appealed the decision.

Defense lawyers filed similar arguments the next day on behalf of more than 400 other migrants, hoping those cases would also be dismissed.

In some cases, prosecutors have been forced to release the men after holding them for months because they had not filed charges.

That occurred in the case of Jesus Manuel Rodriguez Mancha, a welder from Coahuila, Mexico who crossed into Texas in hopes of finding work to support his two children and his mother. He was arrested in September in Kinney County, released three months later to immigration officials and then deported back to Mexico.

“We suffered a lot,” Mr. Rodriguez said in a video interview, describing his experience in a Texas state prison repurposed to hold migrants: poor food, insults from guards, 3 a.m. wake-ups and days on end with little to do and no information about his situation. “They never explained anything,” he said.

In nearby Val Verde County, which has about 47,500 residents and includes Del Rio, where thousands of Haitian migrants huddled under a bridge last fall, the county attorney began dismissing or declining to prosecute most of the trespassing cases. The county has since seen a sharp drop in the number of migrants arrested.

By contrast, officials in Kinney County, where about 3,100 people live in and around one central small town and on vast ranches, have embraced the state-run law-and-order approach to the sharp rise in migrants coming from Mexico, an increase that last year reached levels not seen in more than two decades.

But the three judges who were brought in to assist in hearing hundreds of cases did not always rule in ways that county officials wanted. In many instances, they agreed to release migrants who had been held for months without a hearing, pending a court date. Their replacements have so far denied all requests for such a pretrial release.

As a result, many of the migrants have opted to plead guilty or no contest to the trespassing charges in exchange for an immediate release offered by prosecutors.

“This is the only way they can get a plea out of any of our clients,” said Kristin Etter, a lawyer with Texas RioGrande Legal Aid, speaking of the Kinney County officials.

Mr. Shahan, the Kinney County official, did not respond to a request for comment.

In late November, Mr. Shahan tested positive for the coronavirus and canceled the hearings he was presiding over. In that time, defense lawyers filed more than 150 motions for writs of habeas corpus, an effort to get court hearings for migrants arrested months earlier who had yet to see a judge.

The three retired judges originally assigned by the state to help Kinney County — Vivian Torres, Kitty Schild and Genie Wright — said they could help. “I offered to hear as many of the writs of habeas corpus as could be added to my docket,” Judge Schild said.

Instead of having the judges hear the cases, the county attorney, Brent Smith, filed papers with the Court of Criminal Appeals in Texas seeking to prevent them from granting any more defense motions for hearings or allowing migrants to be released on personal bonds. Mr. Smith wrote that the judges had improperly discussed their cases with defense lawyers via email without including county prosecutors. The judges have denied any impropriety.

“What he said in there were very vague accusations and they weren’t true,” Judge Schild said.

Mr. Smith declined to comment.

The next day, Mr. Shahan informed the judges that their services would “no longer be needed.”

By mid-December, hearings scheduled for Judge Torres were instead presided over by Allen Amos, a former official from another rural county who was picked by Mr. Shahan. Many cases involving migrants who had been arrested in early September featured versions of the same process: a request for pretrial release on a no-fee or personal bond; then a denial by Mr. Amos; then a man, often from Mexico, accepting a guilty plea.

After release, the men would be transferred to the custody of federal immigration officials. Many are quickly deported, but many others end up staying in the United States as they pursue asylum cases.

While a conviction for misdemeanor trespassing alone does not prevent a migrant from applying for asylum, “the purpose of getting them to plead guilty is to have this conviction on their record,” said Anita Gupta, a staff lawyer at the Immigrant Legal Resource Center.

“The goal of Operation Lone Star,” she said, “is to criminalize migrants and then transfer them to Immigration and Customs Enforcement for enforcement and deportation.”