The subphase for the temperature range that lies in between Sm-C(A)* and the three-layer Sm-C(A)* (1/3)subphase has been confirmed to exist using the measurements of electric-field-induced birefringence, optical rotation, and the characteristic reflection bands in the antiferroelectric liquid-crystalline compound, 1-trifluoromethylundecyl-4-(4'-dodecyloxybiphenyl-4-yl-carbonyloxy)-3-fluorobenzoate (12BIMF10). The measurements of electric-field-induced birefringence and optical rotatory power are made on -thick homeotropic cells, and the characteristic reflection bands are observed in free-standing films of thicknesses ranging from 30 to 50 microm. Several binary mixtures have been prepared by mixing (S)-12BIMF10 with (S)-4-(1-methylheptyloxycarbonyl)-phenyl-4'-octylbiphenyl-4-carboxylate (MHPBC), and the effect of racemization of the compound on the character of the biaxial subphase (other than three and four layers) is also discussed. The results are interpreted in terms of the Emelyanenko-Osipov model [Phys. Rev. E 68, 051703 (2003)]; the effective long-range couplings between the director orientations in separated smectic layers emerge after the minimization of free energy with respect to the total (ordinary spontaneous and discrete flexoelectric) polarizations, lifting the degeneracy and producing the nonplanar structures of the subphases.