We investigate the spin rotational structure of magnetic skyrmions in a tetragonal polar magnet VOSe₂O₅ via polarized small-angle neutron scattering (SANS). Spin polarization analysis of the scattered neutrons provides consistent evidence for the cycloidal spin modulation in all the incommensurate phases at zero and non-zero magnetic field along the c axis, including the triangular skyrmion-lattice phase. In the vicinity of the skyrmion phase, we performed extensive SANS measurements to unravel a field-induced incommensurate phase (IC-2 state). We discuss the possibility of anisotropic double-q state as an alternative spin structure to provisional square skyrmion-lattice state.