$q$-Analogues of some supercongruences related to Van Hamme's (E.2) and (F.2) supercongruences

In this paper, we present a one-parameter extension of some supercongruences related to Van Hamme’s $(\mathrm{E}.2)$ and $(\mathrm{F}.2)$ supercongruences. To deduce these results, we first establish the corresponding $q$-supercongruences modulo the third power of a cyclotomic polynomial. Our proofs rely on the \emph{creative microscoping} method devised by Guo and Zudilin~\cite{guo2019q}, together with Jackson’s ${}_6{\phi }_5$ summation formula.