A fire at the seven-story Tower, a residential building in the heart of Montauk’s downtown, on Thursday night caused little damage. The Montauk Fire Department was called following a report of smoke in the basement of the building, which is at 55 South Euclid Avenue, at about 8:25 p.m. The Tower is the tallest building in East Hampton Town, having been built before zoning restrictions on height were in place.The building was immediately evacuated, Mickey Valcich, the Montauk Fire Department’s first assistant chief, said, adding that there were very few residents there at this time of year. No injuries were reported.The fire started in “a shed the size of a dog house,” which is connected to the building and houses various cables, according to Tom Baker, the East Hampton Town fire marshal. He was not able to determine the cause, but said it was not suspicious. The volunteers found heavy smoke on the first floor and in the basement, but there were no flames to be seen by the officers who responded, Mr. Baker said. The smell of smoke was reported up to the third floor. “It was a very small fire, but because of the direction of the wind, it was pushing the smoke into the building. There was no fire in the building, just a lot of smoke,” Mr. Baker said. None of the wires, some of which were for cellphone antennas on the building’s roof, burned, just part of the wooden shed. “It was a pretty smoky event,” he said.The Tower was once known as the Carl Fisher office building, for the developer who built it in in the 1920s when he hoped to make Montauk the Miami Beach of the North.