  Inspired by the recent work on $q$-congruences and the quadratic summation
formula of Rahman, we provide some new $q$-supercongruences. By taking $q\to 1$
in one of our results, we obtain a new Ramanujan-type supercongruence, which
has the same right-hand side as Van Hamme's (G.2) supercongruence for $p\equiv
1 \pmod 4$. We also formulate some related challenging conjectures on
supercongruences and $q$-supercongruences.
