In 2016, Deines, Fuselier, Long, Swisher, and Tu proved that, for any integer \(d\geqslant 3\) and prime \(p\equiv 1\pmod {d}\) , \( \sum _{k=0}^{p-1}(-1)^{dk} {\frac{1-d}{d}\atopwithdelims ()k}^d \equiv -\Gamma _p (\tfrac{1}{d})^d \pmod {p^2}, \) where \(\Gamma _p(x)\) denotes the p-adic Gamma function. They also conjectured that the above congruence holds modulo \(p^3\) . A q-analog of the \(d=3\) case of this congruence modulo \(p^3\) was recently given by Wei and Qin (Mediterr J Math 22:113, 2025). In this paper, we present two q-congruences related to this congruence modulo \(p^3\) for \(d=4\) and \(d=5\) , respectively. Our proofs employ Watson’s \(_8\phi _7\) transformation, the creative microscoping method developed in (Adv Math 346:329–358, 2019), and the Chinese remainder theorem for polynomials.
