This paper proposes a generic platform for topological quantum computation (TQC) using semiconductor heterostructures. The system consists of a semiconductor film with spin-orbit coupling, sandwiched between an s-wave superconductor and a magnetic insulator. This setup enables the existence of non-Abelian Majorana fermions, which are essential for TQC. The key ingredients for non-Abelian statistics are spin-orbit coupling, s-wave superconductivity, and Zeeman splitting, all of which are experimentally realizable in solid-state materials. The paper shows that a semiconductor film with spin-orbit coupling and proximity-induced superconductivity, in the presence of a magnetic insulator, supports zero-energy Majorana fermion modes in the core of an ordinary vortex. The edge of the film forms a chiral Majorana wire due to the breaking of time-reversal symmetry. The system is analyzed using the Bogoliubov de Gennes (BdG) equations, which reveal that the zero-energy state in the m=0 angular momentum channel is non-degenerate and can be used for TQC. The paper also discusses the topological phase transition between a topologically non-trivial and trivial s-wave superconducting phase, determined by the condition (μ² + Δ₀²) < V_z². The quasiparticle gap in the non-trivial phase is governed by the strength of the spin-orbit coupling and the position of the critical point. The system supports a pair of zero-energy Majorana edge modes at the interface between two superconducting layers, which can be used for braiding operations in TQC. The experimental implementation involves a heterostructure of a magnetic insulator, a spin-orbit coupled semiconductor, and an s-wave superconductor. The proposed system is simpler to implement than existing TQC candidates, as it requires standard materials and does not need ultra-low temperatures or high magnetic fields. The paper concludes that this platform provides a straightforward method for the solid-state realization of non-Abelian Majorana fermions.This paper proposes a generic platform for topological quantum computation (TQC) using semiconductor heterostructures. The system consists of a semiconductor film with spin-orbit coupling, sandwiched between an s-wave superconductor and a magnetic insulator. This setup enables the existence of non-Abelian Majorana fermions, which are essential for TQC. The key ingredients for non-Abelian statistics are spin-orbit coupling, s-wave superconductivity, and Zeeman splitting, all of which are experimentally realizable in solid-state materials. The paper shows that a semiconductor film with spin-orbit coupling and proximity-induced superconductivity, in the presence of a magnetic insulator, supports zero-energy Majorana fermion modes in the core of an ordinary vortex. The edge of the film forms a chiral Majorana wire due to the breaking of time-reversal symmetry. The system is analyzed using the Bogoliubov de Gennes (BdG) equations, which reveal that the zero-energy state in the m=0 angular momentum channel is non-degenerate and can be used for TQC. The paper also discusses the topological phase transition between a topologically non-trivial and trivial s-wave superconducting phase, determined by the condition (μ² + Δ₀²) < V_z². The quasiparticle gap in the non-trivial phase is governed by the strength of the spin-orbit coupling and the position of the critical point. The system supports a pair of zero-energy Majorana edge modes at the interface between two superconducting layers, which can be used for braiding operations in TQC. The experimental implementation involves a heterostructure of a magnetic insulator, a spin-orbit coupled semiconductor, and an s-wave superconductor. The proposed system is simpler to implement than existing TQC candidates, as it requires standard materials and does not need ultra-low temperatures or high magnetic fields. The paper concludes that this platform provides a straightforward method for the solid-state realization of non-Abelian Majorana fermions.