We study the weak productions of novel heavy mesons, such as eta'(c), h(c), h'(c), X'(c0), X (3940), Y (3940), X (3872), and Y (4260), in the semileptonic B(c) decays. Since there is still no definite answer for the components of X (3940), Y (3940), X (3872), Y (4260) so far, we will assign them as excited charmonium states with the possible quantum numbers constrained by the current experiments. As for the weak transition form factors, we calculate them in the framework of the light- cone QCD sum rules approach, which has proven to be a powerful tool to deal with the nonperturbative hadronic matrix element. Our results indicate that different interpretations of X ( 3940 ) can result in a remarkable discrepancy of the production rate in the B(c) decays, which would help to clarify the inner structure of the X ( 3940 ) with the forthcoming LHC- b experiments. Besides, the predicted large weak production rates of X ( 3872 ) and Y ( 3940 ) in B(c) decays and the small semileptonic decay rate for B(c) -> Y ( 4260 ) all depend on their quantum number J(PC) assignments. Moreover, the S - D mixing of various vector charmonium states in the weak decay of B(c) is also discussed in this work. The future experimental measurements of these decays will test the inner structures of these particles, according to our predictions here.