We employ the density-dependent cluster model to calculate \(\alpha\) -decay half-lives of recently synthesized superheavy nuclei (SHN) with \(Z=104\) –118. A microscopic \(\alpha\) –nucleus potential is derived via the double-folding method using a realistic nucleon–nucleon interaction. Within the Wentzel–Kramers–Brillouin approximation, supplemented by the Bohr–Sommerfeld quantization condition, we extract both the \(\alpha\) -particle assault frequency and barrier-penetration probability for spherical and deformed daughter configurations. Our predictions for five isotopes of the superheavy element \(Z=123\) are benchmarked against several established models, demonstrating excellent agreement. We also explore the competition between \(\alpha\) -decay and spontaneous fission, and propose likely decay chains for the as-yet unobserved nuclei \({}^{302\text {--}307}123\) . Finally, cluster-decay channels of \({}^{300,303,306,307}123\) are studied using the double-folding potential alongside the Universal curve (UNIV), the Universal Decay Law (UDL), the Unified Decay Formula (UDF), and Horoi’s approach. Notably, the UDL framework predicts positive branching ratios \(\log _{10}b_c\) for heavy-cluster emission (e.g. \(^{90}\textrm{Sr}\) , \(^{96}\textrm{Zr}\) , \(^{102}\textrm{Mo}\) ), indicating that such clusters may rival—or even dominate— \(\alpha\) -decay in these SHN.
