If the arrest was recent
Start with the county jail
Someone who was just arrested in Kansas is almost always in a COUNTY JAIL run by the county sheriff, not in a state prison, so KASPER will not show them.
Kansas has 105 counties, each sheriff running its own jail, and there is no single statewide jail roster.
Some Kansas sheriffs publish an online jail/inmate roster (larger counties such as Sedgwick, Wichita, and Johnson County in the Kansas City metro), but coverage varies and the smallest jails may have nothing online.
The reliable paths for a recent arrest are the arresting county sheriff's jail roster, VINELink, or calling the jail's booking desk.
Kansas has 105 counties, each sheriff running its own jail and roster (some with no online search); there is no unified statewide county-jail search, so use VINELink or the arresting county sheriff.