This Letter presents a search for new light resonances decaying to pairs of quarks and produced in association with a high-$p_{\textrm{T}}$ photon or jet. The dataset consists of proton-proton collisions with an integrated luminosity of 36.1 fb$^{-1}$ at a centre-of-mass energy of $\sqrt{s}=13$ TeV recorded by the ATLAS detector at the Large Hadron Collider. Resonance candidates are identified as massive large-radius jets with substructure consistent with a particle decaying into a quark pair. The mass spectrum of the candidates is examined for local excesses above background. No evidence of a new resonance is observed in the data, which are used to exclude the production of a lepto-phobic axial-vector $Z^\prime$ boson.