This paper studies the coverage path planning and path following problems for an underwater biomimetic robotic fish to finish the deep-sea net cage water quality monitoring. Firstly, with a focus on minimizing total path length, repetition rate, and turning occurrences to enhance path coverage efficiency and reduce energy consumption, we propose a novel coverage path planning strategy. This strategy incorporates DQN, a reward function, and a rewrite strategy inspired by RRT*. Secondly, a high-performance path-following method, which takes into account robot performance, is designed to cope with adverse conditions in net cages. Finally, the simulation and field experiments demonstrate significant improvements over existing methods and the effectiveness in practical applications, showcasing its applicability in aquaculture management. The proposed algorithm offers valuable insights into optimizing coverage path planning for underwater robots in practical scenarios.