Along with π₀ and η mesons, a resonance structure in the invariant-mass spectrum of two photons at M_γγ = 360 ± 7 ± 9 MeV is observed in the reaction dC → γ + γ +X at momentum 2.75GeV/c per nucleon. Estimates of its width and production cross section are Γ = 64 ± 18 MeV and σγγ = 98 ± 24⁺⁹³_-67 μb, respectively. The collected statistics amount to 2339 ± 340 events of 1.5 ∙ 10⁶ triggered interactions of a total number ̴ 10¹² of d+C interactions. This resonance structure is not observed in the γγ channel in ̴ 10¹¹ p+ C collisions at the beam momentum 5.5GeV/c. The result obtained in the reaction d+ C is confirmed by the second experiment carried out on the deuteron beam at momentum 3.83GeV/c per nucleon with a copper target: M = 382 ± 13 MeV, Γ = 62 ± 37 MeV and σ = 273 ± 75 μb. Some results on the observation of the resonance in the invariant-mass spectra of two π⁰ mesons are presented: the data obtained in the d+C→ γ+γ + X reaction is confirmed by the results for the d+C → π⁰ + π⁰ + X and p+C → π⁰ + π⁰ + X reactions; a preliminary estimate of the ratio Br(R→γγ)/Br (R→ π⁰π⁰ is (1.8-3.7) ∙ 10^-3. Further studies of this resonance is assumed at the Nuclotron/NICA at higher setup acceptance, which will allow to elucidate the nature of this resonance by determination of the differential cross sections at different beam energies in the range 1-6GeV/n and the mechanism of its formation.