We employ the Wilf–Zeilberger (WZ) method to establish a proof of a conjecture proposed by Z.-W. Sun, which takes the form of a supercongruence related to p-adic analogues of Ramanujan-type series. By incorporating harmonic numbers and numerous congruence properties, with the help of \(\textit{Sigma}\) package in the software Mathematica, we prove that for any prime \(p>2\) and any positive integer r, \( \frac{1}{p^r}\sum _{n=0}^{p^r-1}\frac{10n+3}{2^{3n}} \left( {\begin{array}{c}2n\\ n\end{array}}\right) ^2\left( {\begin{array}{c}3n\\ n\end{array}}\right) \equiv 3+\frac{49}{8}p^3B_{p-3} \pmod {p^4}, \) where \(B_n\) are Bernoulli numbers given by \( B_0=1,\quad \sum _{k=0}^{n-1}\left( {\begin{array}{c}n\\ k\end{array}}\right) B_k=0\quad (n=2,3,4,\cdots ).\)
