Harnessing solar energy for photocatalytic hydrogen peroxide (H2O2) synthesis represents a pinnacle of environmentally-sensitive and sustainable methodologies. While single-layer crystalline triazine-based organic frameworks (CTFs) are known for their prodigious photocatalytic potential in H2O2 generation, ramifications of the connecting group within the triazine ring (TR) on underlying photocatalytic mechanism warrant deeper exploration. In this study, we simulate three distinct CTFs characterized by different TR linkers: CTF-1 (benzene group (BG)), CTF-2 (horizontally-oriented naphthyl group (NGH)), and CTF-DCN (vertically-oriented naphthyl group (NGV)). These diverse TR linkers profoundly modulate the absorption band edge of CTFs, subsequently dictating the orientation and constitution of the frontier orbitals. Such modulation plays a decisive role in determining the requisite energy for photoexcitation in CTFs, orchestrating the generation and distribution of photo-induced electrons and holes. Remarkably, the NGV linkage imparts CTF-DCN with unparalleled light absorption, superior charge separation efficiency, and the lowest energy barrier for associated reactions. Through this investigation, we illuminate the pivotal influence of TR linkers in sculpting the photocatalytic dynamics of CTFs, providing fresh perspectives for architecting CTFs with amplified photocatalytic prowess in H2O2 synthesis.