The Vernier permanent magnet (VPM) machines supersede conventional permanent magnet synchronous machine (PMSM) topologies in terms of torque-density and cogging torque. This article presents a fractional-slot L-shaped magnet VPM machine, including peculiar designs for permanent magnet (PM) housing and rotor core construction for small-scale EVs such as unmanned aerial vehicles (UAVs). The idea for selecting the PM arrangement is based on combining the V-shaped and spoke-array PM topologies for achieving a higher torque-density than V-shaped PM machines and a lower cogging torque than spoke-array PM machines. The rotor core is created from nonintegrated segments to form the flux-barriers in end-portions of PM housings. In this way, the leakage flux lines in the end-portion of the PMs reduce, resulting in enhanced flux linkage and power factor. A 630 W, 12-slot/8-pole motor is designed and prototyped for model validation purposes. An innovative equivalent magnetic network model is established for analytical prediction of the performance of the machine. The Schwarz–Christoffel mapping is used to create the rotor core permeance network due to its special shaping. Two innovative pentagonal-shaped mesh cells are used in the air-gap region for more accurate capturing of flux behavior. The model is validated by comparing the results with the finite element results and experimental measurements.