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Scattering of charged fermion with $(1+2)$-dimensional wormhole in thepresence of constant axial magnetic flux is explored. By extending the class offermionic solutions of the Dirac equation in the curved space of wormholesurface to include normal modes with real energy and momentum, we found aquantum selection rule for the scattering of fermion waves to the wormhole. Thenewly found {\it momentum-angular momentum relation} implies that only fermionwith the quantized momentum $k=m'/a\sqrt{q}$ can be transmitted through thehole. The allowed momentum is proportional to an effective angular momentumquantum number $m'$ and inversely proportional to the radius of the throat ofthe wormhole $a$. Flux dependence of the effective angular momentum quantumnumber permits us to select fermions that can pass through according to theirmomenta. A conservation law is also naturally enforced in terms of theunitarity condition among the incident, reflected, and transmitted waves. Thescattering involving quasinormal modes~(QNMs) of fermionic states in thewormhole is subsequently explored. It is found that the transmitted wavesthrough the wormhole for all scenarios involving QNMs are mostly suppressed anddecaying in time. In the case of QNMs scattering, the unitarity condition isviolated but a more generic relation of the scattering coefficients isestablished. When the magnetic flux $\phi=mhc/e$, i.e., quantized in units ofthe magnetic flux quantum $hc/e$, the fermion will tunnel through the wormholewith zero reflection.

Scattering of charged fermion to two-dimensional wormhole with constant axial magnetic flux