  The celebrated Erd\H{o}s-Ko-Rado (EKR) theorem for Paley graphs (of square
order) states that all maximum cliques are canonical in the sense that each
maximum clique arises from the subfield construction. Recently, Asgarli and Yip
extended this result to Peisert graphs and other Cayley graphs which are
Peisert-type graphs with nice algebraic properties on the connection set. On
the other hand, there are Peisert-type graphs for which the EKR theorem fails
to hold. In this paper, we show that the EKR theorem of Paley graphs extends to
almost all pseudo-Paley graphs of Peisert-type. Furthermore, we establish the
stability results of the same flavor.
