Havensville is a city in Pottawatomie County, Kansas, United States. As of the 2020 census, the population of the city was 119. Havensville had …Havensville is a city in Pottawatomie County, Kansas, United States. As of the 2020 census, the population of the city was 119. Havensville had its start in the year 1878 by the building of the railroad through that territory. It was named for Paul E. Havens, a railroad employee.