  The aim of this paper is to contribute more examples and classification
results of finite pointed quasi-quantum groups within the quiver framework
initiated in \cite{qha1, qha2}. The focus is put on finite dimensional graded
Majid algebras generated by group-like elements and two skew-primitive elements
which are mutually skew-commutative. Such quasi-quantum groups are associated
to quasi-quantum planes in the sense of nonassociative geomertry \cite{m1, m2}.
As an application, we obtain an explicit classification of graded pointed Majid
algebras with abelian coradical of dimension $p^3$ and $p^4$ for any prime
number $p.$
