The Vernier permanent magnet (VPM) machines supersede conventional permanent magnet synchronous machine (PMSM) topologies in terms of torque-density and cogging torque. This paper 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 non-integrated 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 (EMN) 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.