  We discuss the mass spectrum of $\Omega$ baryon with two heavy quarks and one
light quark (\textit{ccs, bbs and bcs}). The main goal of the paper is to
calculate the ground state masses and after that, the positive and negative
parity excited states masses are also obtained within a Hypercentral
Constituent quark model, using coulomb plus linear potential framework. We also
added first order correction to the potential. The mass spectra upto 5S for
radial excited states and 1P-5P, 1D-4D and 1F-2F states for orbital excited
states are computed for $\Omega_{cc}$, $\Omega_{bb}$ and $\Omega_{bc}$ baryons.
Our obtained results are compared with other theoretical predictions which
could be a useful complementary tool for the interpretation of experimentaly
unknown heavy baryon spectra. The Regge trajectory is constructed in both
($n_r$, $M^{2}$) and ($J$, $M^{2}$) planes for $\Omega_{cc}$,$\Omega_{bb}$ and
$\Omega_{bc}$ baryons and their slopes and intercepts are also determined.
Magnetic moments of doubly heavy $\Omega'$s are also calculated.
