  Magic-angle twisted trilayer graphene (MATTG) recently emerged as a highly
tunable platform for studying correlated phases of matter, such as correlated
insulators and superconductivity. Superconductivity occurs in a range of doping
levels that is bounded by van Hove singularities which stimulates the debate of
the origin and nature of superconductivity in this material. In this work, we
discuss the role of spin-fluctuations arising from atomic-scale correlations in
MATTG for the superconducting state. We show that in a phase diagram as
function of doping ($\nu$) and temperature, nematic superconducting regions are
surrounded by ferromagnetic states and that a superconducting dome with $T_c
\approx 2\,\mathrm{K}$ appears between the integer fillings $\nu =-2$ and $\nu
= -3$. Applying a perpendicular electric field enhances superconductivity on
the electron-doped side which we relate to changes in the spin-fluctuation
spectrum. We show that the nematic unconventional superconductivity leads to
pronounced signatures in the local density of states detectable by scanning
tunneling spectroscopy measurements.
