  We study the boundary criticality enriched by boundary fermions, which
ubiquitously emerge in topological phases of matter, with a focus on
topological insulators and topological superconductors. By employing
dimensional regularization and bosonization techniques, we uncover several
unprecedented boundary universality classes. These include the boundary
Gross-Neveu-Yukawa critical point and the special
Berezinskii-Kosterlitz-Thouless (BKT) transition, both resulting from the
interplay between edge modes and bulk bosons. We present a comprehensive sketch
of the phase diagram that accommodates these boundary criticalities and
delineate their critical exponents. Additionally, we explore a 1+1D conformal
defect decorated with fermions, where a defect BKT transition is highlighted.
We conclude with a discussion on potential experimental realizations of these
phenomena.
