  We study the simplest Lam\'e magnetic superlattice in graphene, finding its
allowed and forbidden energy bands and band-edge states explicitly. Then, we
design quasiperiodic magnetic superlattices supporting bound states using
Darboux transformations. This technique enables us to add any finite number of
bound states, which we exemplify with the most straightforward cases of one and
two bound states in the designed spectrum. The topics of magnetic superlattices
and domain walls in gapped graphene turn out to be connected by a unitary
transformation in the limit of significantly large oscillation periods. We show
that the generated quasiperiodic magnetic superlattices are also linked to
domain walls, with the bound states keeping their nature in such a limit.
