  Conjecture $\mathbb{Z}$ is a knot theoretical equivalent form of the Kervaire
Conjecture. We say that a knot have property $\mathbb{Z}$ if it satisfies
Conjecture $\mathbb{Z}$ for that specific knot. In this work, we show that
alternating Montesinos knots with three tangles have property $\mathbb{Z}$. We
also show that all the pretzel knots of the form $P(p,q,r)$ (not necessarily
alternating) have property $\mathbb{Z}$.
