  We introduce and study the twisted adapted $r$-cluster point and its
combinatorial Auslander-Reiten quivers, called twisted AR-quivers and folded
AR-quivers, of type $A_{2n+1}$ which are closely related to twisted Coxeter
elements and the non-trivial Dynkin diagram automorphism. As applications of
the study, we prove that folded AR-quivers encode crucial information on the
representation theory of quantum affine algebra $U_q'(B^{(1)}_{n+1})$ such as
Dorey's rule and denominator formulas.
