Twisted particles carry Orbital Angular Momentum (OAM), an important property utilized to encode quantum information. The OAM of twisted photons can be trans- ferred onto condensed matter systems in the form of twisted excitons. Numerical solutions of the time-dependent Schr ̈odinger equation for a 3-arm molecular chain are used to demonstrate the manipulation of twisted excitons via an external magnetic field. We present the first design for an OAM transistor in a quasi-1D system that can be used to control the flow of OAM using the magnetic field. The underlying mechanism is the interaction between OAM and the magnetic field which leads to a orbit-resolved Bloch oscillation (ORBO). We present the semi-classical equations of motion for this phenomenon in a one-dimensional system. Unlike classical Bloch oscil- lation, an important effect in ultrafast electron dynamics, the magnet driven ORBO is not limited by electrical breakdown and can easily be observed in natural solids.