Several newq-supercongruences are obtained using transformation formulas for basic hypergeometric series, together with various techniques such as suitably combining terms, and creative microscoping, a method recently developed by the first author in collaboration with Zudilin. More concretely, the results in this paper includeq-analogues of supercongruences (referring top-adic identities remaining valid for some higher power ofp) established by Long, by Long and Ramakrishna, and several otherq-supercongruences. The six basic hypergeometric transformation formulas which are made use of are Watson’s transformation, a quadratic transformation of Rahman, a cubic transformation of Gasper and Rahman, a quartic transformation of Gasper and Rahman, a double series transformation of Ismail, Rahman and Suslov, and a new transformation formula for a nonterminating very-well-poised $${}_{12}\phi _{11}$$12ϕ11 series. Also, the nonterminatingq-Dixon summation formula is used. A special case of the new $${}_{12}\phi _{11}$$12ϕ11 transformation formula is further utilized to obtain a generalization of Rogers’ linearization formula for the continuousq-ultraspherical polynomials.

We establish a new family ofq-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients areq-microscoping and the Chinese remainder theorem for polynomials.

We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q-congruences for truncated basic hypergeometric series with the base being an odd power of q. We also give a number of related conjectures including q-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.

By means of the q-Zeilberger algorithm, we prove a basic hypergeometric supercongruence modulo the fifth power of the cyclotomic polynomial ${\mathrm{\Phi }}_n\left(q\right)$. This result appears to be quite unique, as in the existing literature so far no basic hypergeometric supercongruences modulo a power greater than the fourth of a cyclotomic polynomial have been proved. We also establish a couple of related results, including a parametric supercongruence.