Summary: We consider the magnetic nonlinear Schrödinger equations \[ \begin{aligned} \left(-i\nabla + sA\right)^{2} u + u &= |u|^{p-2} u, \quad p \in (2, 6), \\ \left(-i\nabla + sA\right)^{2}u &= |u|^{4}u,\end{aligned} \] in \(\Omega=\mathcal{O}\times \mathbb{R}\), where \(\mathcal{O}\) is an open subset of \({\mathbb{R}^{2}\setminus\{0\}, s\in\mathbb{R}}\), and \(A:\Omega\rightarrow\mathbb{R}^3\) is the Aharonov-Bohm magnetic potential \[ A(x_{1},x_{2},x_{3}):=\frac{1}{x_{1}^{2}+x_{2}^{2}}(-x_{2},x_{1},0). \] We prove multiplicity results and describe the symmetry properties of the solutions obtained.