  The ground state of QCD with two flavors (up and down quarks) at finite
baryon density in sufficiently strong magnetic field is in a form of either a
chiral soliton lattice(CSL), an array of solitons stacked along the magnetic
field, or a domain-wall Skyrmion phase in which Skyrmions are spontaneously
created on top of the CSL In the latter, one 2D (baby) Skyrmion in the chiral
soliton corresponds to two 3D Skyrmions (baryons) in the bulk. In this paper,
we study spin statistics of topological solitons by using the following two
methods: the conventional Witten's method by embedding the pion fields of two
flavors into those of three flavors with the Wess-Zumino-Witten (WZW) term, and
a more direct method by using the two-flavor WZW term written in terms of a
spin structure. We find that a chiral soliton of finite quantized size called a
pancake soliton and a hole on a chiral soliton are fermions or bosons depending
on odd or even quantizations of their surface areas, respectively, and a
domain-wall Skyrmion is a boson. We also propose surgeries of topological
solitons: a domain-wall Skyrmion (boson) can be cut into a pancake soliton
(fermion) and a hole (fermion), and a chiral soliton without Skyrmions can be
cut into a pancake soliton (fermion) and a hole (fermion).
