Fermions localized on $U(1)$ gauged Q-balls

The axially symmetric $U(1)$ gauged self-interacting Q-balls are shown to support normalizable fermionic bound state, minimally coupled to the electromagnetic field of the Q-ball. It is shown that the effects of the backreaction of the fermionic mode are very small. We explore the domain of existence of the solutions and address some of their physical properties. Among other properties, we observe that the eigenvalue of the Dirac operator remains positive, there is no zero mode in the spectrum.