The Poynting vector associated with the focused vortex beam (FVB) that carries orbital angular momentum (OAM) is oriented in a twisted manner relative to the principal axis of propagation. This characteristic has significant applications in advanced fields, including high-dimensional information processing, high-resolution imaging, and particle manipulation. Currently, complex optical systems that operate on alignment principles for generating FVBs have been miniaturized by metasurfaces, resulting in the achievement of polarization-dependent vectorized behavior. Nevertheless, generating and manipulating FVBs that carry OAM in the terahertz (THz) range remains a significant challenge. This difficulty arises particularly when utilizing quarter-wave plates (QWPs) that serve both polarization conversion and polarization filtering functions. Here, we experimentally demonstrate a planar all-dielectric array capable of generating FVBs with high power density within a single-handed circularly polarized channel. Engineered QWP meta-atoms are utilized as candidates for the efficient generation of the desired FVB through the application of dynamic phase gradients. A series of samples were fabricated to assess the effectiveness of this design strategy in converting an incident linearly polarized THz beam into arbitrary single-handed circularly polarized FVBs. Leveraging the high degree of freedom inherent in polarization multiplexing coding, the proposed QWP metasurface can generate FVBs exhibiting topological charge evolution along the longitudinal direction. This capability further underscores its robust polarization modulation proficiency. This work presents a generalized framework for the polarization-dependent generation of ultracompact structural optical fields, which may have potential applications in highly integrated THz communication systems.