  In this paper, we investigate the properties of the first excited state Dirac
stars (DSs) with higher azimuthal harmonic index (specifically, the azimuthal
harmonic indexes $m_D$ = $3/2$, $5/2$, $7/2$), as well as the relationship
between the ADM mass and angular momentum of Dirac stars with respect to
frequency. Moreover, We find that the ergospheres of DSs appear at lower spinor
field frequencies, and both the ergospheres and the distribution of the spinor
field functions are asymmetric about the equatorial plane. Furthermore, we
introduce the ground state scalar field and examine its impact on this system,
which is known as the multi-state Dirac-boson stars (DBSs) model. We show
various types of solution families for DBSs under both synchronized frequency
$\omega$ and nonsynchronized frequencies and find that similar to DSs, the
spinor field and the ergospheres of DBSs are also asymmetric about the
equatorial plane, but the ergospheres appear at higher spinor field
frequencies.
