We study the production of the exotic charged charmoniumlike state Z(c)(+/-)(3900) in p (p) over bar collisions through the sequential process psi(4260) -> Z(c)(+/-)(3900)(pi)(-/+), Z(c)(+/-)(3900) -> J/psi pi(+/-). Using the subsample of candidates originating from semi-inclusive weak decays of b-flavored hadrons, we measure the invariant mass and natural width to be M = 3902.6(-5.0)(+5.2)(stat)(-1.4)(+3.3)(syst) MeV and Gamma = 32(-21)(+28)(stat)(-7)(+26)(syst) MeV, respectively. We search for prompt production of the Z(c)(+/-)(3900) through the same sequential process. No significant signal is observed, and we set an upper limit of 0.70 at the 95% credibility level on the ratio of prompt production to the production via b-hadron decays. The study is based on 10.4 fb(-1) of p (p) over bar collision data collected by the D0 experiment at the Fermilab Tevatron collider.