Congruences concerning quadrinomial coefficients

In this paper, we establish congruences (mod $p^2$) involving the quadrinomial coefficients ${{\displaystyle \left(\genfrac{}{}{0px}{}{np-1}{p-1}\right)}}_3$ and ${{\displaystyle \left(\genfrac{}{}{0px}{}{np-1}{\frac{p-1}{2}}\right)}}_3$. This is an analogue of congruences involving the trinomial coefficients ${{\displaystyle \left(\genfrac{}{}{0px}{}{np-1}{p-1}\right)}}_2$ and ${{\displaystyle \left(\genfrac{}{}{0px}{}{np-1}{\frac{p-1}{2}}\right)}}_2$ due to Elkhiri and Mihoubi.