Searches for resonant production via a new boson X which decays either to two Higgs bosons (HH) or to one Higgs boson and a new scalar Y (YH), having a mass $m_{\mathrm{Y}} < m_{\mathrm{X}} - m_{\mathrm{H}}$, are presented. The results are based on proton-proton collision data collected by the CMS experiment at the LHC from 2016 to 2018 at a center-of-mass energy of 13 TeV. The data corresponds to an integrated luminosity of 138 ${\rm fb}^{-1}$. The final states considered include a pair of bottom quarks with two W bosons or two photons, and a pair of photons with two $\tau$ leptons. Model independent analyses are performed with a narrow-width approximation for the new boson X in different mass ranges depending on the final states. No evidence for the presence of a signal is observed and corresponding upper limits on the $\mathrm{X \rightarrow HH/YH}$ production cross section are set. Limits are also obtained on the resonant HH production for resonances with spin-0 and spin-2 assumptions in extra dimensions. Both limits on the resonant HH and YH production are interpreted within the MSSM and NMSSM benchmark scenarios, as well as models in the Extended Higgs Sector. Finally, a combination of the results of these searches is provided together with constraints on different beyond the standard model scenarios.