In 2020, Mao and Pan proved a nice result associated with Van Hamme’s (H.2) supercongruence. In the same year, Guo and Zudilin supplied the following generalization of Mao and Pan’s formula: for any odd prime p, \(\begin{aligned} \sum _{k=0}^{(p+1)/2} \frac{(-\frac{1}{2})_k^3}{k!^3} \equiv p\,\dfrac{(\frac{1}{4})_{(p-1)/2}}{(\frac{7}{4})_{(p-1)/2}} {\left\{ \begin{array}{ll} \hspace{-4.5pt}\pmod {p^3} & \text {if }p\equiv 1\pmod 4,\\ \hspace{-4.5pt}\pmod {p^2} & \text {if }p\equiv 3\pmod 4. \end{array}\right. } \end{aligned}\) With the help of the q-Dixon formula, the creative microscoping method, and the Chinese remainder theorem for coprime polynomials, we shall establish a q-supercongruence modulo the third power of a cyclotomic polynomial. When \(q\rightarrow 1\) , it produces the coming generalization of Guo and Zudilin’s supercongruence in the \(p\equiv 3\pmod 4\) case: \(\begin{aligned} \sum _{k=0}^{(p+1)/2}\frac{(-\frac{1}{2})_k^3}{k!^3}\equiv \frac{(\frac{1}{4})_{(p-1)/2}}{(\frac{7}{4})_{(p-1)/2}} \bigg \{p-\frac{p^{3}}{4}H_{(p+1)/4}^{(2)}\bigg \}\pmod {p^3}. \end{aligned}\)
