Context. The study of the distribution, morphology, and kinematics of cold molecular gas in the nuclear and circumnuclear regions of active galactic nuclei (AGNs) helps to characterise and hence to quantify the impact of the AGNs on the host galaxy over its lifetime. Aims. We present the analysis of the molecular gas in the nuclear regions of three Seyfert galaxies, NGC 4968, NGC 4845, and MCG-06-30-15, using Atacama Large sub-Millimetre Array (ALMA) observations of the CO(2−1) emission line. The aim is to determine the kinematics of the gas in the central (∼1 kpc) region and thereby to probe nuclear fueling and feedback of AGNs. Methods. We used two different softwares, namely the 3D-Based Analysis of Rotating Object via Line Observations and DiskFit, to model the kinematics of the gas in the molecular disc, and thereby to determine the gas rotation and any kinematical perturbations. Results. Circular motions dominate the kinematics of the molecular gas in the central discs, mainly in NGC 4845 and MCG-06-30-15; however there is clear evidence of non-circular motions in the central (∼1 kpc) region of NGC 4845 and NGC 4968. The strongest non-circular motion is detected in the inner disc of NGC 4968, mainly along the minor kinematic axis, with a velocity ∼115 km s−1. Of all DiskFit models, the bisymmetric model is found to give the best fit for NGC 4968 and NGC 4845, indicating that the observed non-circular motions in the inner disc of these galaxies could result from the nuclear barred structure, where the gas streams in elliptical orbits aligned along the bar. If the dynamics of NGC 4968 is modelled as a corotation pattern just outside of the bar, the bar pattern speed becomes Ωb = 52 km s−1 kpc−1; the corotation is set at 3.5 kpc; and the inner Lindblad resonance (ILR) ring is R = 300 pc, corresponding to the CO emission ring. In the NGC 4968 galaxy, the torques exerted on the gas by the bar are positive in the centre, within the gas nuclear ring, and negative outside. This shows that the gas is transiently trapped in the ILR. The comparison of the CO intensity maps with the map of the cold dust emission shows an absence of CO in the centre of NGC 4968; also the dust distribution and CO emission in and around the centre of NGC 4845 have similar extensions. The 1.2 mm ALMA continuum is peaked and compact in NGC 4968 and MCG-06-30-15, but their CO(2−1) emissions have extended distributions. Allowing the CO-to-H2 conversion factor αCO between 0.8 and 3.2, which is typical of nearby galaxies of the same type, the molecular mass M(H2) is estimated to be ∼3 − 12 × 107 M⊙ (NGC 4968), ∼9 − 36 × 107 M⊙ (NGC 4845), and ∼1 − 4 × 107 M⊙ (MCG-06-30-15). Conclusions. We conclude that the observed non-circular motions in the molecular disc of NGC 4968 and likely those seen in NGC 4845 are due to the presence of the bar in the nuclear region. We discuss the possibility that the observed pattern in the kinematics might be a consequence of the presence of AGNs, and this might be the case for NGC 4845. At the current spectral and spatial resolution and sensitivity, we cannot claim any strong evidence in these sources of the long sought feedback or feeding effect resulting from the presence of AGNs.