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We report a study of D∗sJ(2317)+ and DsJ(2460)+ meson production in B decays. We observe the decays B+→D(*)+sJ¯¯¯D(*)0 and B0→D(*)+sJD(*)− with the subsequent decays D∗sJ(2317)+→D+sπ0, DsJ(2460)+→D+sγ, and DsJ(2460)+→D*+sπ0. Based on a data sample of 122.1×106 B¯¯¯B pairs collected with the BABAR detector at the PEP-II B factory, we obtain branching …