  Recently, the model of the Einstein-Bardeen theory minimally coupled to a
complex, massive, free scalar field was investigated in arXiv:2305.19057. The
introduction of a scalar field disrupts the formation of an event horizon,
leaving only a type of solution referred to as a Bardeen-boson star. When the
magnetic charge $q$ exceeds a certain critical value, the frozen Bardeen-boson
star can be obtained with $\omega \rightarrow 0$. In this paper, we extend to
the investigation of Einstein-Hayward-scalar model, and obtain the solution of
frozen Hayward-boson star, including the ground and excited states.
Furthermore, under the same parameters, it is interesting to observe that both
the ground state and the excited states frozen stars have the same critical
horizon and mass.
