  We consider certain $K3$-fibered Calabi--Yau threefolds. One class of such
Calabi--Yau threefolds are constructed by Hunt and Schimmrigk using twist maps.
They are realized in weighted projective spaces as orbifolds of hypersurfaces.
Our main goal of this paper is to investigate arithmetic properties of these
Calabi--Yau threefolds. We also consider deformations of our Calabi--Yau
threefolds, and we study the variation of the zeta-functions using $p$-adic
rigid cohomology theory.
