  Using 232 fb-1 of data collected by the BABAR detector, the Xic'+ and Xic'0
baryons are reconstructed through the decays: Xic'+ -> Xic+ gamma and Xic'0 ->
Xic0 gamma, where Xic+ -> Xi- pi+ pi+ and Xic0 -> Xi- pi+. By measuring the
efficiency-corrected yields in different intervals of the center-of-mass
momentum, the production rates from B decays and from the continuum are
extracted. For production from B decays, the branching fractions are found to
be B(B -> Xic'+ X) x B(Xic+ -> Xi- pi+ pi+) = [ 1.69 +- 0.17 (exp.) +- 0.10
(model) ] x 10^-4 and B(B -> Xic'0 X) x B(Xic0 -> Xi- pi+) = [ 0.67 +- 0.07
(exp.) +- 0.03 (model) ] x 10^-4. For production from the continuum the
cross-sections are found to be sigma(e+ e- -> Xic'+ X) x B(Xic+ -> Xi- pi+ pi+)
= 141 +- 24 (exp.) +- 19 (model) fb and sigma(e+ e- -> Xic'0 X) x B(Xic0 -> Xi-
pi+) = 70 +- 11 (exp.) +- 6 (model) fb. The helicity angle distributions of
Xic' decays are studied and found to be consistent with J = 1/2.
