Scale-invariance has rapidly established itself as one of the most used concepts in space plasmas to uncover underlying physical mechanisms via the scaling-law behavior of the statistical properties of field fluctuations. In this work, we characterize the scaling properties of the magnetic field fluctuations in a sub-alfvénic region in contrast with those of the nearby super-alfvénic zone during the ninth Parker Solar Probe perihelion. With our observations, (i) evidence of an extended self-similarity (ESS) for both the inertial and the sub-ion/kinetic regimes during both solar wind intervals is provided, (ii) a multifractal nature of field fluctuations is observed across inertial scales for both solar wind intervals, and (iii) a mono-fractal structure of the small-scale dynamics is reported. The main novelty is that a universal character is found at the sub-ion/kinetic scale, where a unique rescaling exponent describes the high-order statistics of fluctuations during both wind intervals. Conversely, a multitude of scaling symmetries is observed at the inertial scale with a similar fractal topology and geometrical structures between the magnetic field components in the ecliptic plane and perpendicular to it, in contrast with a different level of intermittency, more pronounced during the super-alfvénic interval rather than the sub-alfvénic one, along the perpendicular direction to the ecliptic plane. The above features are interpreted in terms of the possible underlying heating and/or acceleration mechanisms in the solar corona resulting from turbulence and current sheet formation.