Combats at the barriers appeared as part of formal deeds of arms in the late 15th century. Here is an early example hosted by the Chevalier de Bayard at Ayre in Picardy in 1494.
Here is the announcement of a recreation of a combat at the barriers in 2008.
The rules we used.
Here are some of the sources we used for the recreation.
Weapons used at the barriers and examples of barriers combats.
The Tiptoft Rules include rules for barriers combat, probably added in the 16th c.
Here is one way to use scoring cheques for this sort of combat.