JAMESTOWN, NY — In this small town — about as far as one can get from the southern border without entering Canada — residents are bracing for an influx of migrants that could cause a crisis similar to the one that has New York City facing a fiscal cliff.

“If a city of 8 million people can be overwhelmed by a couple thousand migrants, imagine what a couple hundred can do to overwhelm a small rural community upstate?” warned state Sen. Joe Borrello (R-Jamestown).

“It wouldn’t take many migrants to overwhelm the system,” he added.

At least 35 migrants from Colombia are known to have arrived in the tiny upstate city since late last year, with others believed to be living and the shadows and more certainly on the way, a leading Hispanic advocate told The Post.

Locals learned about the new arrivals after a volunteer with the Chautauqua County Hispanic Community Council overheard one speaking with a Colombian accent inside a Tops supermarket last month, council president Max Martin said.

Dan Cappellazzo for NY Post

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Dan Cappellazzo for NY Post

Dan Cappellazzo for NY Post

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The city’s population is 28,393, with 10.6% of it Hispanic, according to the US Census. Until the migrants arrived, the Hispanic community was almost exclusively Puerto Rican, Martin said.

“The Colombians are already here and more are coming. What is the government going to do about it?” Martin asked. “They need housing and transportation or be allowed to work and get a driver’s license.”

But without assistance, Martin warned, “they will have to work illegally to survive.”

“Many of them have already been offered fake Social Security numbers and cards. I worry they may be forced to turn to crime like selling drugs,” he said.

Most of the migrants traveled to Jamestown on their own after learning about the city from fellow border-crossers in El Paso, Texas, several told The Post in Spanish translated by Martin.

“I was in detention for two months,” a migrant named Paola said. “When I was in detention I met a Colombian who told me to come to Jamestown.”

Paola, 29, is sharing a three-bedroom, one-bathroom house with 10 other migrants, including two young children and two teens.

The housemates include a married couple, Mayerly and David, both 23, who work with Paola at a local thrift store where they spoke to The Post.

Mayerly said their house is so crowded that, “I have to make an appointment to use the bathroom.”

“The kids go first in the morning so they can get to school,” she said.

Her husband said they wound up living around 70 miles south of Buffalo because, “At the border, we needed to give them an address of someone who would receive us.”

“A friend told us about Jamestown,” David said. “We spent our last money on a flight from El Paso to Buffalo.”

A 30-year-old woman named Brenda — whose sister is one of the first migrants to have arrived in Jamestown — said she and her two kids followed her sibling there and arrived in November.

“More Colombians are coming to Jamestown,” Brenda said in Spanish. “A family arrived two weeks ago. I know another family with kids coming from Texas now.”

Brenda, who was a nurse in Ibagué, about 50 miles west of the capital of Bogota, said that her husband was “still in the military in Colombia” and that she would “apply for asylum for the security of my children.”

“It is very dangerous in Colombia for my kids because of the gangs,” she said. “There is nothing there for my kids. It is safer here for my kids in Jamestown.”

Brenda and her kids share a run-down house with another migrant named Ricaurte, 52, who said she told him about Jamestown while they were in detention together.

The house is owned by an Amish construction boss who’s friends with Max Martin.

“In immigration, they asked for a phone number of someone in America. I gave them Brenda’s sister’s phone number and address in Jamestown,” Ricaurte said.

Ricaurte said he served in the military under the government that was replaced when leftist former M-19 rebel Gustavo Petro was elected president in June.

“When the new government made a peace treaty with the guerrillas, the guerrillas want to kill the military who was against them. If I stay in Colombia, my life is in danger,” he said.

The Post also visited a three-bedroom, one-bathroom house that’s home to 13 migrants, including six children between 3 and 15, and had three beds in the living room.

During the deadly blizzard that buried the region last month, the place had no heat for three days, most likely due to a frozen gas pipe, said a resident Carlos, 33.

“We put plastic over the windows and wore coats inside,” Carlos said. “The kids kept going to the [hot air] vents, looking for warmth.”

Carlos said his wife and two daughters lived with him there until he sent them away from the cramped conditions to stay with his wife’s brother in Chicago.

“I’m worried I won’t be able to afford rent. I don’t want my kids to be homeless,” he said.

Carlos, who worked as a construction worker in Ibagué, said he didn’t “want to take a chance on working illegally because I risk being deported.”

And if he went to Chicago, Carlos said, “I’m afraid I might have to start the immigration process all over again. My papers say Jamestown.”

Martin, the community council president, said, “It has been a shock to see the amount of Latinos from Colombia coming to Jamestown.”

“The reason is the open border,” he said. “I would do the same thing, by the way, because of the freedom and opportunity we have in America. You can come here poor and become rich if you work your butt off.

“The cold weather and the language barrier won’t make them leave,” he added.

Democratic Jamestown Mayor Eddie Sundquist didn’t immediately respond to an interview request from The Post.

But Republican Chautauqua County Executive PJ Wendel said he was concerned by the situation unfolding in Jamestown and had sought help from Gov. Kathy Hochul and US Senate Majority Leader Chuck Schumer (D-NY), whose assistants didn’t offer any.

“Even if it’s 100 families, our school districts are small,” Wendel said. “Those schools don’t have the resources. If they don’t have a Spanish teacher, what are they going to do?”

Wendel added: “It could be overwhelming for us because how are we supposed to be helping these people?”

Spokespeople for Hochul and Schumer didn’t immediately return requests for comment.