  Osburn, Sahu and Straub introduced the numbers: \begin{align*}
A_n^{(r,s,t)}=\sum_{k=0}^n{n\choose k}^r{n+k\choose k}^s{2k\choose n}^t,
\end{align*} for non-negative integers $n,r,s,t$ with $r\ge 2$, which includes
two kinds of Ap\'ery numbers and four kinds of Ap\'ery-like numbers as special
cases, and showed that the numbers $\{A_n^{(r,s,t)}\}_{n\ge 0}$ satisfy the
Gauss congruences of order $3$. We establish an extension of
Osburn--Sahu--Straub congruence through Bernoulli numbers, which is one step
deep congruence of the Gauss congruence for $A_n^{(r,s,t)}$.
