1st Cavalry Regiment, Fort Leavenworth, Kansas Territory. Operations against the Cheyenne and against rabid abolitionists terrorizing the territory. Wounded July 1857 in skirmish with Cheyenne during a saber charge under his commander Sumner.
While seeking re-appointment with the Quartermaster dept, in Washington, DC, he volunteered to accompany R.E. Lee as aide-de-camp to Harper’s Ferry to secure the arsenal there. A man calling himself Isaac Smith led the group holding the arsenal. From his experiences fighting in Bleeding Kansas, he recognized and identified “”Old Ossawatomie Brown”—ie. John Brown.
It is a matter of public record. Not “the movies” of fantasist looney visions.
I don't see any evidence that Stuart was fighting John Brown in Kansas.
The army arrived after the Battle of Black Jack to restore order, but I don't see where it took sides or participated in the warfare.