AbstractUsing a sample of $1.31\times 10^{9} ~J/ψ $1.31×109J/ψ events collected with the BESIII detector, we perform a study of $J/ψ → γ K{\bar{K}}η '$J/ψ→γKK¯η′. X(2370) is observed in the $K{\bar{K}}η '$KK¯η′ invariant-mass distribution with a statistical significance of $8.3σ $8.3σ. Its resonance parameters are measured to be $M=2341.6± 6.5 \, \text {(stat.)} ± 5.7 \, \text {(syst.)}~ \hbox {MeV}/c^{2}$M=2341.6±6.5(stat.)±5.7(syst.)MeV/c2 and $Γ = 117± 10 \, \text {(stat.)}± 8 \, \text {(syst.)}~\hbox {MeV}$Γ=117±10(stat.)±8(syst.)MeV. The product branching fractions for $J/ψ → γ X(2370),X(2370)→ K^{+}K^{-}η '$J/ψ→γX(2370),X(2370)→K+K-η′ and $J/ψ → γ X(2370),X(2370)→ K_{S}^{0}K_{S}^{0}η '$J/ψ→γX(2370),X(2370)→KS0KS0η′ are determined to be $(1.79± 0.23\, \text {(stat.)}± 0.65\,\text {(syst.)})\times 10^{-5}$(1.79±0.23(stat.)±0.65(syst.))×10-5 and $(1.18± 0.32\, \text {(stat.)}± 0.39\, \text {(syst.)})\times 10^{-5}$(1.18±0.32(stat.)±0.39(syst.))×10-5, respectively. No evident signal for X(2120) is observed in the $K{\bar{K}}η '$KK¯η′ invariant-mass distribution. The upper limits for the product branching fractions of ${\mathcal {B}}(J/ψ → γ X(2120)→ γ K^{+} K^{-} η ')$B(J/ψ→γX(2120)→γK+K-η′) and ${\mathcal {B}}(J/ψ → γ X(2120)→ γ K_{S}^{0} K_{S}^{0} η ')$B(J/ψ→γX(2120)→γKS0KS0η′) are determined to be $1.49\times 10^{-5}$1.49×10-5 and $6.38\times 10^{-6}$6.38×10-6 at the 90% confidence level, respectively.