  Based on our revised perturbational-band theory, we study possible pairing
states driven by interaction in the electron-doped quasicrystal
30\degree-twisted bilayer graphene. Our mean-field study on the related t-J
model predicts that, the beneath-van-Hove and beyond-van-Hove low doping
regimes are covered by the chiral $d+id$ and $g+ig$ topological
superconductivities (TSCs) respectively. The $g+ig$-TSC possesses a pairing
angular momentum 4, and hence following each effective $C_{12}$- rotation by
$\Delta\phi=n\pi/6$, the pairing phase changes $4\Delta\phi$. This intriguing
TSC is novel, as it belongs to a special 2D $E_4$- irreducible representation
of the effective $D_{12}$ point group unique to this quasicystal and absent on
periodic lattices. The Ginzburg-Landau theory suggested that the $g+ig$- TSC
originates from the Josephson coupling between the $d+id$ pairings on the two
mono-layers.
