Photoluminescence, its excitation power dependence, and Raman scattering spectra have been studied in CdSe/ZnS and CdSeTe/ZnS QDs for the nonconjugated states and after the QD conjugation to the anti-Interleukin-10, Human papilloma virus and Pseudo rabies virus antibodies. The QD bioconjugation to charged antibodies stimulates the "blue" energy shift of PL bands related to exciton emission in the CdSe or CdSeTe cores. The "blue" energy shift of PL spectrum in bioconjugated CdSe/ZnS QDs has been attributed to the electronic quantum confined effects stimulated by decreasing the effective QD size at its bioconjugation to charged antibodies. It was shown that the attachment of a charge deals with the antibody to the exterior shell of CdSe/ZnS QDs, leads to blocking away a fraction of core's volume. The energy band diagrams of CdSeTe/ZnS QDs in the nonconjugated and bioconjugated states have been designed, which permit to explain the types of optical transitions in QDs and their transformations at the QD bioconjugation. It is shown that the change of energy band profile and the "blue" shift of QD energy levels, owing to the change of potential barrier at the QD surface, are the dominant reasons of PL spectrum transformation in the double core CdSeTe/ZnS QDs conjugated to charged antibodies. Better understanding the QD bioconjugation to specific antibodies is expected to produce the major advances in biology and medicine and can be a powerful technique for early medical diagnostics.