This presentation will cover the branching fraction measurements of chi_cJ -> phi phi (J=0,1,2), eta_c(2S) -> pi+ pi- eta, chi_cJ -> Omega+ antiOmega- (J=0,1,2), and psi(3770) -> eta J/psi. The first three measurements are benefitted from the huge psi(2S) samples collected at BESIII and the transitions from psi(2S) to chi_cJ or eta_c(2S). The last one is based on e+ e- annihilation data sample collected at c.m.s 3.773 GeV. The branching fractions of the decays chi_cJ -> phi phi (J=0,1,2) have been measured most precisely, and the polarization parameters of chi_cJ -> phi phi have been determined for the first time via a helicity amplitude analysis. The evidence of eta_c(2S) -> pi+ pi- eta has been found in the decay sequence psi(3686) -> gamma eta_c(2S), eta_c(2S) -> pi+ pi- eta for the first time.The decays chi_cJ -> Omega+ anti-Omega- (J=0,1,2) have been observed for the first time with high significance, respectively, and the relevant branching fractions have been provided.The process e+ e- -> eta J/psi at a center-of-mass energy 3.773 GeV is observed for the first time, its Born cross-section is measured, and the branching fraction of psi(3770) -> eta J/psi is determined by a combined fit with the cross-sections at other energy points, after considering the interference effect for the first time.