Using 3 fbˉ1 of proton-proton collisions, collected at centre-of-mass energies of √s = 7 and 8 TeV by the LHCb detector, several measurements of charmless B⁰s meson decays are made. A search is also performed for a highly suppressed B⁰ decay. First, the branching fraction of the B0⁰s→ ØØ decay is measured to be B(B⁰s→ ØØ) = (1.84 ± 0.05(stat) ± 0.07(syst) ± 0.11(fs=fd) ± 0.12(norm))X10ˉ⁵; where the third and fourth uncertainties arise from the fragmentation fraction fs/fd and the branching fraction of the normalisation mode. This represents a factor of five reduction in the statistical uncertainty compared to the previous best measurement. An upper limit on the branching fraction of the mode B⁰→ ØØ is set at B(B⁰→ ØØ) < 2.8 X 10ˉ⁸ (90% CL). This is a factor of seven improvement over the previous best measurement. An amplitude analysis of the B⁰s→ ØK+Kˉ decay is performed, wherein first observations of the decay modes B⁰s→ Øf´2(1525) and B⁰s→ ØØ(1680) are made. The branching fraction of the B⁰s→ Øf´2(1525) decay is measured to be B(B⁰s→ Øf´2 (1525)) = (1.63 ± 0.18(stat) ± 0.12(syst) ± 0.29(model) ± 0.17(norm)) X 10ˉ⁶; where the 'model' uncertainty arises from the choice of amplitude model. The longitudinal polarisation fraction of the decay B⁰s→ Øf´2(1525) is measured to be F0 = (86.6 ± 3.4 ± 0.8 ± 2.0 (model))%.