  Detailed timing analyses of three cataclysmic variables, namely 2MASS
J09213414$-$5939068, IGR J16167$-$4957, and V667 Pup are carried out using the
long-baseline and high-cadence optical photometric data from the Transiting
Exoplanet Survey Satellite (TESS). Periods of 908.12$\pm$0.05 s and
990.10$\pm$0.06 s are observed in the optical variation of 2MASS
J09213414$-$5939068 that were not found in earlier studies and appear to be
probable spin and beat periods of the system, respectively. The presence of
multiple periods at spin, beat, and other sidebands indicates that 2MASS
J09213414$-$5939068 likely belongs to an intermediate polar class of magnetic
cataclysmic variables that seems to be accreted via a disc-overflow mechanism.
Clear evidence of a period of 582.45$\pm$0.04 s is found during the TESS
observations of IGR J16167$-$4957, which can be interpreted as the spin period
of the system. Strong modulation at this frequency supports its classification
as an intermediate polar, where accretion may primarily be governed by a disc.
The dominance of the spin pulse unveils the disc-fed dominance accretion in
V667 Pup, but the detection of the previously unknown beat period of
525.77$\pm$0.03 s suggests that a portion of the material is also accreted
through a stream. Moreover, the double-peaked structure observed in the optical
spin pulse profile of V667 Pup suggests the possibility of a two-pole accretion
geometry, where each pole accretes at a different rate and is separated by
180$^\circ$.
