The B0sπ± invariant mass distribution is investigated in order to search for possible exotic meson states. The analysis is based on a data sample recorded with the LHCb detector corresponding to 3 fb−1 of pp collision data at √s=7 and 8 TeV. No significant excess is found, and upper limits are set on the production rate of the claimed X(5568) state within the LHCb acceptance. Upper limits are also set as a function of the mass and width of a possible exotic meson decaying to the B0sπ± final state. The same limits also apply to a possible exotic meson decaying through the chain B*0sπ±, B*0s→B0sγ where the photon is excluded from the reconstructed decays.Received 2 August 2016Corrected 6 March 2017DOI:https://doi.org/10.1103/PhysRevLett.117.152003Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.© 2016 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)Research AreasBranching fractionHadronic decaysQuantum chromodynamicsPhysical SystemsBottom mesonsExotic mesonsParticles & Fields