  We present a theory of superconductivity in magic-angle twisted bilayer
graphene and analyze the superconducting phase diagram in presence of the
magnetic field. Namely, we consider a model of a granular array hosting
localized states, which are hybridized via the delocalized fermions in the
inter-grain regions. We study a strong coupling situation when the interactions
lead to an incoherent state with preformed Cooper pairs inside the grains. The
Andreev scattering among different grains manifests itself through the global
phase-coherent superconducting state at lower temperatures. We demonstrate that
a new phase transition between the preformed Cooper pairing state and the
Larkin-Ovchinnikov-Fulde-Ferrell state might be induced by the spin
pair-breaking effect of in-plane magnetic field. The upper critical magnetic
field is shown to be enhanced in the strong coupling case.
