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We perform the first amplitude analysis of D^+ₛ ^+^+^-⁰ decays, based on data samples of electron-positron collisions recorded with the BESIII detector at center-of-mass energies between 4. 128 and 4. 226 GeV, corresponding to an integrated luminosity of 7. 33~fb^-1. We report the observation of Dₒ^+ f₀ (980) (770) ^+ with a statistical significance greater than 10 and determine the branching fractions B (Dₛ^+^+^+^-⁰| ₍₎₍-) = (2. 040. 08 ₒₓ₀ₓ. 0. 05 ₒₘₒₓ. ) \% and B (Dₛ^+^+) = (1. 560. 09 ₒₓ₀ₓ. 0. 04 ₒₘₒₓ. ) \%. Moreover, we measure the relative branching fraction between ^+^-⁰ and K^+K^- to be B ( (1020) ^+^-⁰) B ( (1020) K^+K^-) =0. 230 0. 014 ₒₓ₀ₓ. 0. 010 ₒₘₒₓ. , which deviates from the world average value by more than 4.
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