Did Jesse James the out law ever get caught?

Yes, Jesse James, the infamous outlaw, was ultimately killed rather than captured. He was shot by Robert Ford, a member of his own gang, on April 3, 1882, in St. Joseph, Missouri. Ford aimed to collect the reward for James and to gain notoriety, but his actions led to widespread condemnation. James's criminal activities had eluded law enforcement for many years prior to his death.