We report the thermal and dielectric investigations on a liquid crystal exhibiting an antiferroelectric phase and confined in a polymer network of sub-micron dimensions. Two different photo-polymerizable monomers have been employed for the purpose: one of them (HDDA) is bereft of any aromatic parts, while the other (RM82) contains aromatic as well as aliphatic units and, in fact, forms a liquid crystalline phase in its monomeric state. The polymerization, which is carried out in the presence of the liquid crystalline host, is expected to yield a nanosegregated structure for HDDA and blended structure for the RM82 case, the difference reflecting the morphologies of the networks, as evidenced by SEM images. Surprisingly, even a small concentration of the latter polymer added to the former variety has substantial influence on the morphology. The main work focusses on calorimetry and dielectric relaxation spectroscopy of the host liquid crystal confined in these nanonetworks created by the polymers, which can be considered to form virtual surfaces with a finite anchoring energy. We have investigated the in-phase and antiphase modes in the antiferroelectric phase, and the soft mode in the paraelectric phase preceding the antiferroelectric phase. The relaxation frequencies of all these modes are substantially influenced by the network, with the results showing certain surprises in cases containing both HDDA and RM82.