Aftershocks following the mainshock frequently induce secondary structural damage. Although connected buildings feature distinctive configurations with complex force-transfer mechanisms under seismic loads, they are designed without considering aftershock effects. This study employs incremental dynamic analysis to investigate the seismic fragility of a connected structure under a mainshock and mainshock-aftershock sequences. Fragility differences are compared, and the impact of artificial mainshock-aftershock sequences constructed by different methods on the seismic fragility of the structure is analyzed. Results demonstrate that the fragility curves of the structure under mainshock-aftershock sequences lie above those under an isolated mainshock. Aftershocks increase the exceedance probabilities of limit states by average increments of 4.15%, 6.12%, and 4.9% under frequent, fortification, and rare earthquakes, respectively. The fragility of the structure differs across various types of mainshock-aftershock sequences. The fragility under the artificial mainshock-aftershock constructed by the decay method is closest to that under natural mainshock-aftershock and exhibits the smallest exceedance probability. By contrast, the structure under the mainshock-aftershock constructed by the repetition-based method shows the largest exceedance probability. The average differences between the maximum and minimum exceedance probabilities are 3.9%, 5.32%, and 4.06% under frequent, fortification, and rare earthquake intensity levels, respectively. Artificial mainshock-aftershock sequences exhibit greater damage potential than natural sequences, with those constructed by the repetition-based method demonstrating the most significant destructive effects. Under mainshock-aftershock sequences, the connected structure largely meets the seismic fortification objectives. However, the detrimental effects of aftershocks must still be appropriately considered in future designs.