In this paper, we study extended modules for a special class of Ore extensions. We will assume that $R$ is a ring and $A$ will denote the Ore extension $A:=R[x_1, \ldots, x_n:\sigma]$ for which $\sigma$ is an automorphism of $R$, $x_ix_j = x_jx_i$ and $x_ir = \sigma(r)x_i$, for every $1 \leq i,j \leq n$. With some extra conditions over the ring $R$, we will prove Vaserstein’s, Quillen’s patching, Horrocks’, and Quillen–Suslin’s theorems for this type of non-commutative rings.