What name was given to the fight over slavery in the kansas territory in the mid-1800’s?

The fight over slavery in the Kansas territory in the mid-1800s was called "Bleeding Kansas".

Explanation:

Bleeding Kansas refers to the events in the Kansas Territory from 1855 to 1859 that took place in the context of political struggles over the possible introduction of slavery. These conflicts were accompanied by atrocities, some of which were politically motivated and others were committed in the context of robberies. The politically motivated conflicts in the Kansas Territory are seen as a precursor to the Civil War.