  Inspired by the recent observations of $B$ and $B_s$ meson states at
LHCb\cite{Aaij:2020hcw} we calculate the masses of ground, orbitally, and
radially excited states. Also, we estimate the mixing parameters, decay
constant, leptonic decay width, and corresponding branching ratios, as well as
electromagnetic transition widths. ${\cal{O}}\left(\frac{1}{m}\right)$ and
${\cal{O}}(p^{10})$ relativistic corrections to potential and kinetic energy
terms have been added to the Hamiltonian. The screening potential employed is
solved by applying the gaussian wave function. The estimated masses are used to
construct the Regge trajectories, which help us in the association of some
newly observed states to $B$ and $B_s$ meson family. Overall, the results from
the present study are in fair agreement with available experimental and
theoretical studies.
