  For an oriented $3$-manifold $M$, let $\mathcal{S}(M)$ denote its Kauffman
bracket skein module over $\mathbb{Z}[q^{\pm\frac{1}{2}}]$. It is shown that
$\mathcal{S}(M)$ admits infinitely many torsion elements when $M$ is the
exterior of the Montesinos knot $K(a_1/b_1,a_2/b_2,a_3/b_4,a_4/b_4)\subset S^3$
with each $b_i\ge 3$. This provides a negative answer to Problem 1.92 (G)-(i)
in the Kirby's list, which asks whether $\mathcal{S}(M)$ is free when $M$ is
irreducible and has no incompressible non-boundary parallel torus.
