  Topological holography is a conjectured correspondence between the symmetry
charges and defects of a $D$-dimensional system with the anyons in a
$(D+1)$-dimensional topological order: the symmetry topological field theory
(SymTFT). Topological holography is conjectured to capture the topological
aspects of symmetry in gapped and gapless systems, with different phases
corresponding to different gapped boundaries (anyon condensations) of the
SymTFT. This correspondence was previously considered primarily for bosonic
systems, excluding many phases of condensed matter systems involving fermionic
electrons. In this work, we extend the SymTFT framework to establish a
topological holography correspondence for fermionic systems. We demonstrate
that this fermionic SymTFT framework captures the known properties of $1+1D$
fermion gapped phases and critical points, including the classification,
edge-modes, and stacking rules of fermionic symmetry-protected topological
phases (SPTs), and computation of partition functions of fermionic conformal
field theories (CFTs). Beyond merely reproducing known properties, we show that
the SymTFT approach can additionally serve as a practical tool for discovering
new physics, and use this framework to construct a new example of a fermionic
intrinsically gapless SPT phase characterized by an emergent fermionic anomaly.
