The application of energy band theory in optics provides an effective approach to modulating the flow of light. The recent discovery of non-Hermitian skin effect promotes the development of traditional energy band theory, which further enables an alternative way to realize light localization and unidirectional propagation. However, how to effectively generate and steer the non-Hermitian skin effect is still an important topic, especially in integrated optical systems. Here, we investigate the non-Hermitian skin effect in quasi-one-dimensional rhombic optical lattice with synthetic gauge potential. By calculating the eigenenergy spectra, spectral winding number, and wave dynamics, the gauge potential can be utilized to effectively tune the localization strength of skin modes. In particular, the skin effect is completely suppressed when the gauge potential in each plaquette is equal to π, while the flat-band localization caused by Aharonov-Bohm caging effect is dominant. By utilizing the indirectly coupled micro ring resonator array, the gauge potential and asymmetric coupling can be generated at the same time, which provides a potential experimental scheme to explore the competition between Aharonov-Bohm cage and skin effect. The present study provides an alternative way to steer the skin effect, which offers an approach to achieving the on-chip non-magnetic unidirectional optical devices.