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Fan-spine magnetic structure, as a fundamental three-dimensional topology in magnetic reconnection theory, plays a crucial role in producing solar jets. However, how fan-spine configurations form in the solar atmosphere remains elusive. Using the Chinese H$\alpha$ Solar Explorer (CHASE) and the Solar Dynamics Observatory (SDO), we present a case study on the complete buildup of fan-spine topology driven by flux emergence and the subsequent jet production. Two fan-spine structures and the two associated null points are present. Variations in null-point heights and locations were tracked over time during flux emergence. The north fan-spine structure is found to be created through magnetic reconnection between the newly emerged flux and the background field. Gentle reconnection persistently occurs after formation of the north fan-spine structure, resulting in weak plasma outflows. Subsequently, as flux emergence and magnetic helicity injection continue, the formation and eruption of mini-filaments after reconnection at the quasi-separatrix layer between the two nulls trigger three homologous jets. The CHASE observations reveal that the circular flare ribbon, inner bright patch, and remote brightening all exhibit redshifted signatures during these jet ejections. This work unveils the key role of flux emergence in the formation of fan-spine topology, and highlights the importance of mini-filaments for subsequent jet production.

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