Employing the q-Lucas theorem and some known q-supercongruences, we give some Dwork-type q-congruences, confirming three conjectures in [J. Combin. Theory, Ser. A 178 (2021), Art. 105362]. As conclusions, we obtain the following supercongruences: for any prime \(p\equiv 1\pmod {4}\) and positive integer r, \(\begin{aligned} \sum _{k=0}^{(p^r-1)/2} \frac{(\frac{1}{2})_k^3}{k!^3}&\equiv -\Gamma _p(\tfrac{1}{4})^4 \sum _{k=0}^{(p^{r-1}-1)/2} \frac{(\frac{1}{2})_k^3}{k!^3} \pmod {p^{r+1}}, \\ \sum _{k=0}^{p^r-1} \frac{(\frac{1}{2})_k^3}{k!^3}&\equiv -\Gamma _p(\tfrac{1}{4})^4 \sum _{k=0}^{p^{r-1}-1} \frac{(\frac{1}{2})_k^3}{k!^3} \pmod {p^{r+1}}, \end{aligned}\) where \((x)_n=\Gamma (x+n)/\Gamma (x)\) , and \(\Gamma _p(x)\) stands for the p-adic Gamma function. The first one confirms a weaker form of Swisher’s (H.3) conjecture for \(p\equiv 1\pmod {4}\) , which originally predicts that the supercongruence is true modulo \(p^{3r}\) .
