Evidence of strong coupling of quasiparticle excitations with γ-vibration is shown to occur in transitional nuclei. High-spin band structures in 166,168,170,172 Er are studied by employing the recently developed multiquasiparticle triaxial projected shell model approach. It is demonstrated that a low-lying K = 3 band observed in these nuclei, the nature of which has remained unresolved, originates from the angular-momentum projection of triaxially deformed two-quasiparticle (qp) configurations. Further, it is predicted that the structure of this band depends critically on the shell filling: in 166 Er the lowest K = 3 2-qp band is formed from proton configuration, in 168 Er the K = 3 neutron and proton 2-qp bands are almost degenerate, and for 170 Er and 172 Er the neutron K = 3 2-qp band becomes favored and can cross the γ-vibrational band at high rotational frequencies. We consider that these are few examples in even-even nuclei, where the three basic modes of rotational, vibrational, and quasi-particle excitations co-exist close to the yrast line.