Dust particles are often electrostatically trapped and levitated within the non-electroneutral region of a sheath. The fascinating transport phenomena of dust particles strongly depend on the plasma parameters surrounding them within the sheath, whereas, that are quite difficult to obtain, leading to an unclear understanding of particle transport mechanisms. Here, we demonstrate a tunable horizontal transport of micron-sized dust particles by precisely manipulating their vertically suspended heights in an asymmetric ratchet sheath by designing dusty plasma ratchet. A collection of dust particles serves as micro-probes to detect the height-dependent transport properties and the feature of the sheath. Two methods are employed to lift or reduce the suspended heights of dust particles while maintaining the sheath unchanged. As the suspended heights of dust particles vary, their directional transport changes accordingly, including a flow reversal. A two-dimensional model of the ratchet sheath depicts the nonlinear distributions of plasma parameters and reveals that these unexpected transport phenomena can be attributed to the dependence of the electric ratchet potential and the resulting non-equilibrium net ion drag force on the suspended heights of dust particles. Our combined experimental and theoretical study provides insights into the fundamental transport properties of dust particles in an asymmetrical sheath.