Polycrystalline samples of double perovskites Ba2BOsO6 (B = Sc, Y, In) were synthesized by solid state reactions. They adopt the cubic double perovskite structures (space group, Fm-3m) with ordered B and Os arrangements. Ba2BOsO6 (B = Sc, Y, In) show antiferromagnetic transitions at 93 K, 69 K, and 28 K, respectively. The Weiss-temperatures are -590 K for Ba2ScOsO6, -571 K for Ba2YOsO6, and -155 K for Ba2InOsO6. Sc3+ and Y3+ have the open-shell d0 electronic configuration, while In3+ has the closed-shell d10. This indicates that a d0 B-type cation induces stronger overall magnetic exchange interactions in comparison to a d10. Comparison of Ba2BOsO6 (B = Sc, Y, In) to their Sr and Ca analogues shows that the structural distortions weaken the overall magnetic exchange interactions.