The spelling of the town where Oliver Smith was born is probably Quenemo, rather than the spelling you showed. It is in Osage County. Since he was born in 1881 I would encourage you to read Osage County census for 1880 (in case he wasn't the oldest child) and the 1885 Kansas State census which should show him. The Kansas State Historical Society will loan the microfilmed 1885 census to your library at no charge. Good luck to you.