  We establish quasi-two-dimensional thin films of iron-based superconductors
(FeSCs) as a new high-temperature platform for hosting intrinsic
time-reversal-invariant helical topological superconductivity (TSC). Based on
the combination of Dirac surface state and bulk extended $s$-wave pairing, our
theory should be directly applicable to a large class of experimentally
established FeSCs, opening a new TSC paradigm. In particular, an applied
electric field serves as a "topological switch" for helical Majorana edge modes
in FeSC thin films, allowing for an experimentally feasible design of
gate-controlled helical Majorana circuits. Applying an in-plane magnetic field
drives the helical TSC phase into a higher-order TSC carrying corner-localized
Majorana zero modes. Our proposal should enable the experimental realization of
helical Majorana fermions.
