  The Kondo effect describes the spin-exchanging interaction between localized
impurity and the itinerant fermions. The ultracold alkaline-earth atomic gas
provides a natural platform for quantum simulation of the Kondo model,
utilizing its long-lived clock state and the nuclear-spin exchanging
interaction between the clock state and the ground state. One of the key issue
now is whether the Kondo temperature can be high enough to be reached in
current experiment, for which we have proposed using a transverse confinement
to confine atoms into a one-dimensional tube and to utilize the
confinement-induced resonance to enhance the Kondo coupling. In this work, we
further consider the $1+0$ dimensional scattering problem when the clock state
is further confined by an axial harmonic confinement. We show that this axial
confinement for the clock state atoms not only plays a role for localizing
them, but also can act as an additional control knob to reach the
confinement-induced resonance. We show that by combining both the transverse
and the axial confinements, the confinement-induced resonance can be reached in
the practical conditions and the Kondo effect can be attainable in this system.
