Fractures are widely distributed in coal, and studying the seepage characteristics of fluids in fractures is of great significance for unconventional natural gas extraction and prevention of gas disasters. In this work, based on the W-M fractal function, a Y-shaped fracture model with different roughness is established. The seepage characteristics of Y-shaped fracture with different roughness are interpreted from two perspectives. Firstly, the seepage law of the Y-shaped fracture with the same roughness is studied. Secondly, the fluid competitive diversion capacity caused by the difference of branch fracture roughness is discussed. The results show that the fracture roughness is an important factor affecting the seepage characteristics of the fracture. When the roughness of the fracture is identical, the outlet flow rate, velocity, and Re are all positively correlated with pressure, and the flow regime is unchanged. The increase in the fracture roughness will lead to a significant flow rate and momentum loss, resulting in maximum loss up to 45.44%, besides, enhance the flow resistance of the fracture, Re increasing by 771, 713, 489, and 355, respectively, at four patterns. And there is a threshold DM between 1.1 and 1.2 so that the major influencing factor on hydraulic conductivity changes. In addition, the roughness difference between the branch fractures of the Y-shaped fracture is the key factor to control the fluid competitive diversion capacity. The larger the roughness difference, the greater difference in flow velocity, and the more significant change in flow rate proportion, which proportion differs by 4%, 44%, and 54%, respectively, and the stronger smooth branch fracture competitive diversion capacity, and the lower the rough branch fracture hydraulic conductivity. As the inlet pressure increases, the two branch fractures Re gradually increases but Eu decreases, which Eu in smooth branch fracture is smaller is 15, 19, 20, and 21 smaller than that of rough branch, respectively, and the rough branch fracture competitive diversion capacity is weakened. Both roughness difference and inlet pressure will affect the competitive diversion capacity of the Y-shaped fracture. These results are expected to provide new insights for the exploitation of underground fluid resources.