Abstract A structure is observed in the $${B} ^{\pm }{K} ^{\mp }$$ B ± K ∓ mass spectrum in a sample of proton–proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, collected with the LHCb detector and corresponding to a total integrated luminosity of 9 $$\,\text {fb} ^{-1}$$ fb - 1 . The structure is interpreted as the result of overlapping excited $${B} ^0_{s} $$ B s 0 states. With high significance, a two-peak hypothesis provides a better description of the data than a single resonance. Under this hypothesis the masses and widths of the two states, assuming they decay directly to $${B} ^{\pm }{K} ^{\mp }$$ B ± K ∓ , are determined to be $$\begin{aligned} m_1&= 6063.5 \pm 1.2 \text { (stat)} \pm 0.8\text { (syst)}\,\text {Me}\text {V}, \\ \Gamma _1&= 26 \pm 4 \text { (stat)} \pm 4\text { (syst)}\,\text {Me}\text {V}, \\ m_2&= 6114 \pm 3 \text { (stat)} \pm 5\text { (syst)}\,\text {Me}\text {V}, \\ \Gamma _2&= 66 \pm 18 \text { (stat)} \pm 21\text { (syst)}\,\text {Me}\text {V}. \end{aligned}$$ m 1 = 6063.5 ± 1.2 (stat) ± 0.8 (syst) Me , Γ 1 = 26 ± 4 (stat) ± 4 (syst) Me , m 2 = 6114 ± 3 (stat) ± 5 (syst) Me , Γ 2 = 66 ± 18 (stat) ± 21 (syst) Me . Alternative values assuming a decay through $${B} ^{*\pm }{K} ^{\mp }$$ B ∗ ± K ∓ , with a missing photon from the $$B^{*\pm } \rightarrow B^{\pm }\gamma $$ B ∗ ± → B ± γ decay, which are shifted by approximately 45 $$\,\text {Me}$$ Me V, are also determined. The possibility of a single state decaying in both channels is also considered. The ratio of the total production cross-section times branching fraction of the new states relative to the previously observed $$B_{s2}^{*0}$$ B s 2 ∗ 0 state is determined to be $$0.87 \pm 0.15 \text { (stat)} \pm 0.19 \text { (syst)}$$ 0.87 ± 0.15 (stat) ± 0.19 (syst) .