  A moir\'{e} pattern occurs when two periodic structures in a system have a
slight mismatch period, resulting the coexistence of distinct phases in
different large-scale spacial regions of the same system. Two periodic
structures can arise from periodic electric and magnetic fields, respectively.
We investigated the moir\'{e} pattern via a dimerized Kitaev spin chain with a
periodic transverse field, which can be mapped onto the system of dimerized
spinless fermions with p-wave superconductivity. The exact solution for
staggered field demonstrated that the ground state has two distinct phases: (i)
Neel magnetic phase for nonzero field, (ii) Spin liquid phase due to the
emergence of isolated flat Bogoliubov--de Gennes band for vanishing field. We
computed the staggered magnetization and local density of states
(\textrm{LDOS}) for the field with a slight difference period to the chain
lattice. Numerical simulation demonstrated that such two phases appear
alternatively along the chain with a long beat period. Additionally, we
proposed a dynamic scheme to detect the Moir\'{e} fringes based on the
measurement of Loschmidt echo (\textrm{LE}) in the presence of local
perturbation.
