High electron mobility transistors (HEMTs) based on a wider bandgap AlGaN channel prove more efficient for high-voltage operation. The significant advantages of AlGaN channel HEMTs include a high critical electric field and higher saturation velocity. These characteristics contribute substantially to expanding the operating regime of power electronics, making them more suitable for applications requiring high voltage. This research work introduces a novel structure for a HEMT based on AlGaN/GaN with a recessed Gamma (Γ)-gate. The proposed HEMTs are composed of a 30 nm supply/barrier layer and an 18 nm channel layer, constructed on a Beta Gallium Oxide (BGO) substrate. Additionally, a delta-doped layer is incorporated to enhance device characteristics. The Direct Current (DC) features of the introduced scheme are compared with those of Γ-gate, rectangular and T-gate configurations, and analyzed using Silvaco TCAD software under various considerations. Key parameters including threshold voltage and transconductance are extracted from the DC characteristics. The proposed device provides a comparable cut-off frequency of 998 GHz for 20 nm gate length. Finally, the thermal efficiency of the introduced scheme, utilizing lateral lattice thermal conductivity, results in peak temperatures of 398.2 K, demonstrating superior performance compared to existing gate structures. The optimized performance of the device is assessed against existing devices, demonstrating its superiority among the compared schemes.