We present the results of a detailed timing analysis of observations of Cen X-3 taken by the University of Durham Mark 6 imaging atmospheric Cherenkov telescope in 1997-1999. The presence of a TeV gamma -ray signal at the overall >= 4.5sigma significance level in the ``fully cut'' image selected data, as reported earlier, is confirmed. A search for possible modulations of gamma -rays with the pulsar spin period P0~ 4.8 s was performed by the step-by-step application of image parameter cuts of gradually increasing hardness. The data of each of 23 days of observations have not revealed any statistically significant Rayleigh power peak, except for 1 day when a peak with a chance probability p=6.8x 10-7 was found in ``soft-cut'' data sets. This modulation, if real, is blue shifted by 6.6 ms (>103 km s-1) from the nominal second harmonic of the X-ray pulsar. Taking the large number of frequency trials into account, the estimated final probability of finding such a peak by chance still remains = 100 MeV) and very high energy (VHE, E>= 100 GeV) gamma -rays. We propose on the basis of the energetics required that all reasonable options for the gamma -ray production in Cen X-3 must be connected to jets emerging from the inner accretion disc around the neutron star. One of the principal options is a large-scale source, with R_s ~ 1013 - 1014 cm; this assumes effective acceleration of electrons up to ~ 10 TeV by shocks produced by interaction of these jets with the dense atmosphere of the binary. It is shown that such a quasi-stationary model could explain the bulk of the gamma -radiation features observed except for the gamma -ray modulations with the pulsar spin. These modulations, if genuine, would require an alternative source with R_s << 1011 cm. We consider two principal models, hadronic and leptonic, for the formation of such a compact source in the jet. Both models predict that the episodes of pulsed gamma -ray emission may be rather rare, with a typical duration not exceeding a few hours, and that generally the frequency of pulsations should be significantly shifted from the nominal frequency of the X-ray pulsar. The opportunities to distinguish between different models by means of future gamma -ray observations of this X-ray binary are also discussed
