Doctors in West Texas are seeing measles patients whose illnesses have been complicated by an alternative therapy endorsed by vaccine skeptics including Robert F. Kennedy Jr., the health secretary.

Parents in Gaines County, Texas, the center of a raging measles outbreak, have increasingly turned to supplements and unproven treatments to protect their children, many of whom are unvaccinated, against the virus.

One of those supplements is cod liver oil containing vitamin A, which Mr. Kennedy has promoted as a near miraculous cure for measles. Physicians at Covenant Children’s Hospital in Lubbock, Texas, say they’ve now treated a handful of unvaccinated children who were given so much vitamin A that they had signs of liver damage.

Some of them had received unsafe doses of cod liver oil and other vitamin A supplements for several weeks in an attempt to prevent a measles infection, said Dr. Summer Davies, who cares for acutely ill children at the hospital.

“I had a patient that was only sick a couple of days, four or five days, but had been taking it for like three weeks,” Dr. Davies said.

While doctors sometimes administer high doses of vitamin A in a hospital to manage severe measles, experts do not recommend taking it without physician supervision. Vitamin A is not an effective way to prevent measles; however, two doses of the measles, mumps and rubella vaccine are about 97 percent effective.

At high doses, vitamin A can cause liver damage; dry, peeling skin; hair loss; and, in rare instances, seizures and coma. So far, doctors at West Texas hospitals have said they’ve seen patients with yellowed skin and high levels of liver enzymes in their bloodwork, both signs of a damaged liver.

Many of those patients had been in the hospital for a severe measles infection; doctors discovered the liver damage only after routine lab work.

As of Tuesday, the outbreak, which began in January, had spread to more than 320 people in Texas. Forty patients have been hospitalized, and one child has died.

In neighboring New Mexico counties, the virus has sickened 43 and hospitalized two. Seven confirmed cases in Oklahoma have also been linked to the outbreak.

Local doctors and health officials have become increasingly concerned about the growing popularity of unproven remedies for preventing and treating measles, which they fear is causing people to delay critical medical treatment and to reject vaccination, the only proven way to prevent a measles infection.

In Gaines County, alternative medicine has always been popular. Many in the area’s large Mennonite community, where most cases have been clustered, avoid interacting with the medical system and adhere to a long tradition of natural remedies.

Health officials said the recent popularity of vitamin A use for measles could be traced back to a Fox News interview with Mr. Kennedy, in which he said he had heard of “almost miraculous and instantaneous recovery” with treatments like cod liver oil, which he said was “the safest application of vitamin A.”

In an opinion essay for The Washington Post on Tuesday afternoon, Kevin Griffis, who was until last week the communications director at the Centers for Disease Control and Prevention, wrote that he had resigned in part because of Mr. Kennedy’s handling of the outbreak.

“In my final weeks at the C.D.C., I watched as career infectious-disease experts were tasked with spending precious hours searching medical literature in vain for data to support Kennedy’s preferred treatments,” Mr. Griffis wrote.

In the weeks after the Fox News interview, drugstores in West Texas struggled to keep vitamin A and cod liver oil supplements on their shelves. “I did not hear anything about vitamin A until he said it on television,” said Katherine Wells, the director of public health in Lubbock.

One local doctor — whom Mr. Kennedy named in the Fox News interview as one of the physicians who had told him “what is working on the ground”— opened a makeshift clinic in Gaines County and began doling out various treatments, including vitamin A supplements, to treat active measles cases and to prevent infection.

Dr. Davies said she suspected that a majority of the children she had treated had taken vitamin A supplements at home.

Experts say that vitamin A can play an important role in the “supportive care” that doctors provide to patients with severe measles infections.

It works by replenishing the bodily stores depleted by the virus, which bolsters the immune system, said Dr. William Schaffner, an infectious disease specialist at Vanderbilt University Medical Center.

In the hospital, physicians give only two doses of the vitamin to children with measles, usually over the course of two days, and “very carefully calibrate” the amounts depending on age and weight, he said.

Dr. Schaffner emphasized that it is not a miracle treatment for the virus, and that there is no antiviral medication for measles. And there is no credible evidence that vitamin A helps prevent infection in children in the United States, where vitamin A deficiencies are exceedingly rare.

In fact, giving children repeated, high doses of the vitamin is dangerous. Unlike other vitamins, which are flushed out of the body through urine, excess vitamin A accumulates in fat tissue, making it more likely to reach dangerous levels over time.

“That kind of preventative use I think is especially concerning,” said Dr. Lara Johnson, another doctor at the Lubbock hospital.

“When we have kids taking it for weeks and weeks, then you do potentially have a cumulative impact of the toxicity,” she added.

Dr. Johnson added that local physicians were particularly concerned about parents’ relying on over-the-counter supplements — whose labels don’t always accurately reflect the amount of vitamin they contain — and accepting dosage recommendations from unverified sources.