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A bstract Using data collected with the BESIII detector in  e  +  e   −   collisions at center-of-mass energies between 4.178 and 4.226 GeV and corresponding to 6.32 fb  − 1  of integrated luminosity, we report the amplitude analysis and branching-fraction measurement of the    $$ {D}_s^{+} $$  D s + → π  +  π  0  η ′ decay. We find that the dominant intermediate process is    $$ {D}_s^{+} $$  D s + → ρ  +  η ′ and the significances of other resonant and nonresonant processes are all less than 3 σ . The upper limits on the branching fractions of  S -wave and  P -wave nonresonant components are set to 0.10% and 0.74% at the 90% confidence level, respectively. In addition, the branching fraction of the    $$ {D}_s^{+} $$  D s + → π  +  π  0  η ′ decay is measured to be (6 . 15  ±  0 . 25(stat . )  ±  0 . 18(syst . ))%, which receives significant contribution only from    $$ {D}_s^{+} $$  D s + → ρ  +  η ′ according to the amplitude analysis.

Amplitude analysis and branching-fraction measurement of $$ {\mathrm{D}}_{\mathrm{s}}^{+} $$ → π+π0η′