  We investigate the Andreev reflection and Josephson effect in the $\alpha$-T3
lattice which falls between graphene ($\alpha = 0$) and the dice lattice
($\alpha = 1$) by adjusting the parameter $\alpha$. In the regime of specular
Andreev reflection, when the incident energy of electron is small, the
probability of Andreev reflection decreases as the parameter $\alpha$
increases. On the contrary, when the incident energy is large, the probability
of Andreev reflection increases as the parameter $\alpha$ increases.
Interestingly, when the incident energy approaches the superconducting
energy-gap function, the Andreev reflection with approximate all-angle perfect
transmission happens in the case of $\alpha = 1$. In the regime of Andreev
retro-reflection, when the parameter $\alpha$ increases, the probability of
Andreev reflection increases regardless of the value of incident energy. When
the incident energy approaches the superconducting energy-gap function, the
Andreev reflection with approximate all-angle perfect transmission happens
regardless of the value of $\alpha$. We also give the differential conductance
in these two regimes and find that the differential conductance increases as
the parameter $\alpha$ increases generally. In addition, the $\alpha$-T3
lattice-based Josephson current increases as $\alpha$ increases. When the
length of junction approaches zero, the critical Josephson currents in the
different values of $\alpha$ approach the same value.
