Given a finite extension $\mathbf{K/F}$ of degree $r$ of a finite field $\mathbf{F}$ in characteristic $p$, we enumerate all selfdual skew cyclic codes in the Ore quotient ring $\mathbf{E}_{k}:=\mathbf{K}[X^{\pm 1};\Frob]/(X^{kr}-1)$ for any positive integer ${k}$ coprime to the characteristic $p$. We use a new approach based on vector space duality, which establishes an order reversing and orthogonality preserving bijection between skew codes and vector subspaces. Finally we implement this enumeration in SageMath.