A search for the exotic decay of the Higgs boson () into a resonance plus missing transverse momentum is described. The search is performed with the ATLAS detector at the Large Hadron Collider using 139 of collisions at TeV. The search targets events from production in an NMSSM scenario where , with , where is a light pseudoscalar Higgs boson and are the two lightest neutralinos. The decay of the boson into a pair of -quarks results in a peak in the dijet invariant mass distribution. The final-state signature consists of two leptons, two or more jets, at least one of which is identified as originating from a -quark, and missing transverse momentum. Observations are consistent with Standard Model expectations and upper limits are set on the product of cross section times branching ratio for a three-dimensional scan of the masses of the , and boson.