Illinois and your home state of Kansas are both members of the Drivers License Compact (DLC) meaning that the IL Secretary of State office or the traffic court will notify the Kansas Department of Revenue about this speeding citation if you plead guilty and pay the fine.

According to the KS DOR there is a place on your driving record for the court or DMV to note the State of occurrence / State of offense when moving violations are placed on there so it would appear that the IL speeding ticket would be placed on your Kansas driver's history.

To see if you can get the speeding ticket reduced or dismissed by taking a driving course or traffic school you would need to discuss this with the Illinois court listed on your ticket. Traffic school might be an option and the IL court would be able to tell you if there is an online one that you could take from your home in Kansas.