Agro-residues constitute the largest reservoir of renewable carbon source on Earth. While their valorization has primarily focused on cellulose, hemicellulose is the second most abundant group of polysaccharides and remains underexploited. Glycosyl hydrolases (GHs) are key enzymes involved in the depolymerisation of plant biomass, and filamentous fungi are widely recognized as efficient producers of GHs enzymes. In the present study, an in-house isolate, Aspergillus fumigatus PSF1, was used to produce xylanase via solid-state fermentation (SSF) with wheat bran as the sole carbon source. Key process conditions, including moisture percent, inoculum load, temperature, and pH, were initially optimized using the One-Factor-at-a-Time (OFAT) method and subsequently statistically optimized using Response Surface Methodology (RSM). Under optimized conditions, xylanase activity reached 147.96 IU gds^-1, a 1.29-fold increase relative to unoptimized conditions. The study demonstrates that systematic optimization of critical fermentation parameters significantly enhances xylanase productivity in SSF by A. fumigatus PSF1. The findings suggest that wheat bran is an effective low-cost substrate and highlight the potential of this fungal strain for scalable, high-yield xylanase production.