A structure is observed in the {B} ^{pm }{K} ^{mp } 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}. The structure is interpreted as the result of overlapping excited {B} ^0_{s} 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 }, are determined to be m1=6063.5±1.2(stat)±0.8(syst)Me,Γ1=26±4(stat)±4(syst)Me,m2=6114±3(stat)±5(syst)Me,Γ2=66±18(stat)±21(syst)Me.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} m_1&= 6063.5 \\pm 1.2 \\text { (stat)} \\pm 0.8\\text { (syst)}\\,\\text {Me}\\text {V}, \\\\ \\Gamma _1&= 26 \\pm 4 \\text { (stat)} \\pm 4\\text { (syst)}\\,\\text {Me}\\text {V}, \\\\ m_2&= 6114 \\pm 3 \\text { (stat)} \\pm 5\\text { (syst)}\\,\\text {Me}\\text {V}, \\\\ \\Gamma _2&= 66 \\pm 18 \\text { (stat)} \\pm 21\\text { (syst)}\\,\\text {Me}\\text {V}. \\end{aligned}$$\\end{document}Alternative values assuming a decay through {B} ^{*pm }{K} ^{mp }, with a missing photon from the B^{*pm } rightarrow B^{pm }gamma decay, which are shifted by approximately 45,text {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} state is determined to be 0.87 pm 0.15 text { (stat)} pm 0.19 text { (syst)}.