An amplitude analysis of flavor-untagged B_{s}^{0}→J/ψpp[over ¯] decays is performed using a sample of 797±31 decays reconstructed with the LHCb detector. The data, collected in proton-proton collisions between 2011 and 2018, correspond to an integrated luminosity of 9 fb^{-1}. Evidence for a new structure in the J/ψp and J/ψp[over ¯] systems with a mass of 4337_{-4}^{+7} _{-2}^{+2} MeV and a width of 29_{-12}^{+26} _{-14}^{+14} MeV is found, where the first uncertainty is statistical and the second systematic, with a significance in the range of 3.1 to 3.7σ, depending on the assigned J^{P} hypothesis.