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The study of confinement in quantum spin chains has seen a large surge of interest in recent years. It is not only important for understanding a range of effective one-dimensional condensed-matter realizations but it also shares some of the nonperturbative physics with quantum chromodynamics (QCD), which makes it a prime target for current quantum simulation efforts. In analogy to QCD, the confinement-induced two-particle bound states that appear in these models are dubbed mesons. Here, we study scattering events due to meson collisions in a quantum spin chain with long-range interactions such that two mesons have an extended interaction. We show how novel hadronic bound states, e.g., with four constituent particles akin to tetraquarks, may form dynamically in fusion events. In a natural collision their signal is weak, as elastic meson scattering dominates. However, we propose two controllable protocols that allow for a clear observation of dynamical hadron formation. We discuss how this physics can be simulated in trapped-ion or Rydberg-atom setups.