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Let $\mathbb{T}$ be the unit circle and $\Gamma \backslash G$ the$3$-dimensional Heisenberg nilmanifold. We prove that a class of skew productson $\mathbb{T} \times \Gamma \backslash G$ are distal, and that the M\"{o}biusfunction is linearly disjoint from these skew products. This verifies theM\"{o}bius Disjointness Conjecture of Sarnak.

M\"{o}bius disjointness for skew products on a circle and a nilmanifold