We determine the strong converse exponent for the entanglement cost of quantum state merging, showing that it is characterized by the optimized $α$-$z$ conditional Rényi entropies with $z=α/2\in[1/2,1]$. This contrasts with the sandwiched conditional Rényi entropies that typically govern strong converse exponents in quantum information theory. As a consequence, we derive the strong converse exponent of the partially smoothed conditional min-entropy in purified distance. This exponent is governed by club-sandwiched conditional entropies, whereas global smoothing leads to a sandwiched expression.

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