<p>Fermionic many-body systems provide a setting to investigate how interactions drive collective quantum behaviour, including macroscopic coherence and superfluidity. Central to these phenomena is the formation of Cooper pairs, correlated states of two fermions that behave as composite bosons and condense below a critical temperature. Unlike elementary bosons, these pairs retain an internal structure determined by the underlying fermionic correlations, which is essential for understanding superfluid properties across the crossover from Bose–Einstein condensation to Bardeen–Cooper–Schrieffer crossover. Here we use a sonic analogue of the optical Sagnac effect to probe the composite nature of fermionic condensates across this crossover. We realize an in situ loop interferometer by coherently exciting two counter-propagating long-wavelength phonons of an annular fermionic superfluid with tuneable interactions. By injecting a quantized supercurrent into the superfluid ring, we lift the frequency degeneracy between clockwise and anticlockwise sound modes. The resulting Doppler shift allows us to probe the elementary quantum of circulation and the angular momentum per particle in the fermionic fluid. Our observations reveal that superflow circulation is quantized in units determined by fermion pairs, providing access to the superfluid fraction of the unitary Fermi gas in the low-temperature regime. Our results establish phonon interferometry as a probe of strongly correlated quantum systems.</p>