U(1) extension of the Standard Model (SM) is well motivated, where the charges of SM fermions are fixed by gauge anomaly cancellations and Yukawa interactions. While the literature extensively discusses anomaly cancellation solutions in which SM fermions are vector-like under new \(U(1)_X \) symmetry, allowing the Yukawa structure to remain invariant, chiral solutions in which SM fermions are chiral under new symmetry are not well explored. In this work, we venture into these relatively unexplored chiral solutions. We presented a particularly intriguing chiral solution with the introduction of three right-handed fermions (RHFs). We termed this symmetry as Dark-Hyper Charge (DHC) Symmetry. This terminology stems from the resemblance of the \(U(1)_X\) charges of the SM particles to hypercharge, with the term ‘dark’ referring to the relatively large charges of the RHFs. This implies that the branching fraction of \(Z'\) to these RHFs should be significantly high. The introduced RHFs could potentially serve as Dark Matter (DM) candidates. We will demonstrate in a model-independent manner using only the \(Z'\) interaction channel, that the lightest RHF, denoted as \(F_{1}\) , is a viable DM candidate, and it can meet all current DM constraints with a mass of \(M_{F_{1}} \gtrsim 150\) GeV.