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Based on our revised perturbational-band theory, we study possible pairingstates driven by interaction in the electron-doped quasicrystal30\degree-twisted bilayer graphene. Our mean-field study on the related t-Jmodel predicts that, the beneath-van-Hove and beyond-van-Hove low dopingregimes are covered by the chiral $d+id$ and $g+ig$ topologicalsuperconductivities (TSCs) respectively. The $g+ig$-TSC possesses a pairingangular momentum 4, and hence following each effective $C_{12}$- rotation by$\Delta\phi=n\pi/6$, the pairing phase changes $4\Delta\phi$. This intriguingTSC is novel, as it belongs to a special 2D $E_4$- irreducible representationof the effective $D_{12}$ point group unique to this quasicystal and absent onperiodic lattices. The Ginzburg-Landau theory suggested that the $g+ig$- TSCoriginates from the Josephson coupling between the $d+id$ pairings on the twomono-layers.

$g+ig$ topological superconductivity in the 30$^o$-twisted bilayer graphene