This paper presents a novel linear hybrid excited flux switching permanent magnet machine (LHEFSPMM) with a crooked tooth modular stator. Conventional stators are made up of a pure iron core, which results in high manufacturing costs and increased iron core losses. Using a modular stator lowers the iron volume by up to 18% compared to a conventional stator, which minimizes the core losses and reduces the machine’s overall cost. A crooked angle is introduced to improve the flux linkage between the stator pole and the mover slot. Ferrite magnets are used with parallel magnetization to reduce the cost of the machine. Two-dimensional FEA is performed to analyze and evaluate various performance parameters of the proposed machine. Geometric optimization is used to optimize the split ratio (S.R) and winding slot area (Slotarea). Genetic algorithm (GA) is applied and is used to optimize stator tooth width (STW), space between the modules (SS), crooked angle (α), and starting angle (θ). The proposed model has a high thrust density (306.61 kN/m3), lower detent force (8.4 N), and a simpler design with higher efficiency (86%). The linear modular structure makes it a good candidate for railway transportation and electric trains. Thermal analysis of the machine is performed by FEA and then the results are validated by an LPMEC model. Overall, a very good agreement is observed between both the analyses, and relative percentage error of less than 3% is achieved, which is considerable since the FEA is in 3D while 2D temperature flow is considered in the LPMEC model.