<p>We introduce a specific deformed Bose gas model, whose underlying quasiparticle algebra is related to the <i>κ</i>-deformed bosonic oscillator algebra. We then develop the statistical distribution function of a gas model of the <i>κ</i>-deformed bosons containing finite and infinite dimensional cases. We investigate interpolating statistics behavior of this deformed model and apply it to lattice oscillations via the Debye crystal model. The effect of the deformation parameter <i>κ</i> onto the low-temperature behavior of the model specific heat is discussed and is compared with the results of both the standard phonon gas and the ones with the Tsallis non-extensive statistics. Another application is carried out onto the Bose-like condensation of this deformed model and the conditions under which the <i>κ</i>-deformed boson condensation would occur in such a system are discussed. It is shown that the critical temperature of the <i>κ</i>-deformed boson gas with the infinite dimensional case is higher than that of the ideal Bose gas, while it has lower values than those of the ideal Bose gas for the finite dimensional case. We consider that the results obtained in this work may provide much physical insight into further studies on strongly correlated quantum materials as well as interacting theories of bosons including collective excitations, where unconventional quantum statistics might have an important role.</p>