Non-trivial band topology along with magnetism leads to different novel quantum phases. When time-reversal symmetry is broken in three-dimensional topological insulators (TIs) through, e.g., the proximity effect, different phases such as the quantum Hall phase or the quantum anomalous Hall(QAH) phase emerge, displaying interesting transport properties for spintronic applications. The QAH phase displays sidewall chiral edge states, which leads to the QAH effect. We have considered a heterostructure consisting of a TI, namely Bi[Formula: see text]Se[Formula: see text], sandwiched between two two-dimensional ferromagnetic monolayers of CrI[Formula: see text], to study how its topological and transport properties change due to the proximity effect. Combining DFT and tight-binding calculations, along with non-equilibrium Green's function formalism, we show that a well-defined exchange gap appears in the band structure in which spin-polarised edge states flow. In a finite slab, the nature of the surface states depends on both the cross-section and thickness of the system. Therefore, we also study the width and finite-size effects on the transmission and topological properties of this magnetised TI nanoribbon.