The natural surface roughness of clay pores is evident, particularly after hydraulic fracturing in shale gas formations. The impact of this roughness becomes increasingly pronounced when transitioning from the macroscale to the nanoscale pores. The presence of rough particles poses a hindrance to fluid flow, causing alterations in flow states along the rough lines. However, there is limited exploration of clay nanopores characterized by rough surfaces and exposed edges. In this work, molecular dynamics simulations are used to investigate the two-phase flow on rough surface driven by different pressure gradients. For that, three different chain illite particles, called A, B, and C, are constructed based on the White's edge structure theory. The roughness of clay illite pores is modelled by three protruding illite particles distributed on the surface. Through the study of flow state, shear rate and flow flux, it is found that rough surfaces, in contrast to smooth clay surfaces, induce a blocking effect on two-phase flow. At low pressure gradients, methane molecules in the center of the pores traverse water bridges, while un-displaced methane molecules accumulate at the edge of illite rough particles. This traversal significantly influences the velocity distribution in two-phase flow, and the adsorption exemplifies the blocking effect of the rough surface. Notably, the A chain surface exhibits the most pronounced blocking effect on clay surface fluids compared to B and C chain surfaces. The edges of illite rough particles contribute substantial velocity perpendicular to the pore surface during two-phase flow, while reducing the distance between opposing pore surfaces, which is conducive to the generation of water bridges and impedes the methane transport. At high pressure gradients, all three illite particles detach from the clay surface, resulting in a significant increase in flux. This work provides a molecular understanding of two-phase flow in rough illite nanopores and offers a foundational understanding for future endeavors in the construction of clay nanopore roughness.