This work presents comprehensive analysis of a A$l_{\mathrm{x}}Ga_{(1-x)}$N/GaN High Electron Mobility Transistor(HEMT) biosensor for variation in A$l_{\mathrm{x}}Ga_{(1-x)}$N layer alloy composition, bulk trap and doping for sensing a wide set of biomolecule charge. For this study, biomolecular interface charges in the order 1$0^{12}/c\mathrm{m}^{2}$, 1$0^{13}/c\mathrm{m}^{2}$,1$0^{14}/c\mathrm{m}^{2}$ and 1$0^{15}/c\mathrm{m}^{2}$ are preferred which are exhibited by some especially significant and recognized biomarkers like the breast cancer biomarker (c-erbB-2), Kidney injury Molecule (KIM-I), Monokine Induced by Interferon Gamma (MIG) and Prostate Specific Antigen (PSA) at diverse environments. The impact of A$l_{\mathrm{x}}Ga_{(1-x)}$N layer mole fraction, trap and doping are assessed by quantifying changes in energy band, electron concentration in 2D Electron Gas (2DEG), potential distribution, current-voltage characteristics and sensitivity. Multifold changes in sensitivity are noted with change in A$l_{\mathrm{x}}Ga_{(1-x)}$N layer composition benefitting from changing polarization at A$l_{\mathrm{x}}$Ga(1-x)N/GaN surface, whereas, rate of such change differs considerably for each order of biomolecular interface charges. It is further found that presence of acceptor bulk trap and ntype doping in A$l_{\mathrm{x}}Ga_{(1-x)}$N heavily modifies the sensitivity for lower biomolecular interface charges of order 1$0^{12}/c\mathrm{m}^{2}$,1$0^{13}/c\mathrm{m}^{2}$ (induced by c-erbB-2, KIM-I) but yield minor effect on sensitivity for higher biomolecular interface charges of order 1$0^{14}/c\mathrm{m}^{2},10^{15}/c\mathrm{m}^{2}$ (induced by MIG, PSA).