This study presents a comprehensive modeling of wakefield generation through external injection utilizing a Laguerre-Gaussian (LG) laser beam in a bubble/blowout regime. The wakefield dynamics are simulated in two dimensions using the particle-in-cell (2D-PIC) method via Wake-T tool, aiming to investigate the underlying mechanisms and characteristics of this process. The simulation results provide insights into the behavior of electrons within the wakefield, their acceleration, phase spaces of the electron beam, velocity distribution, and longitudinal and transversal profiles of the laser electric field in the plasma. The presented model serves as a valuable tool for further investigations into wakefield generation with external injection using LG laser beams, facilitating advancements in this field of study.