We report results of a study of doubly charmed baryons and charmed strange baryons. The analysis is performed using a 980 fb^-1 data sample collected with the Belle detector at the KEKB asymmetric-energy e^+e^- collider. We search for doubly charmed baryons Xi_cc^+(+) with the Lambda_c^+K^-pi^+(pi^+) and Xi_c^0pi^+(pi^+) final states. No significant signal is observed. We also search for two excited charmed strange baryons, Xi_c(3055)^+ and Xi_c(3123)^+ with the Sigma_c^++(2455)K^- and Sigma_c^++(2520)K^- final states. The Xi_c(3055)^+ signal is observed with a significance of 6.6 standard deviations including systematic uncertainty, while no signature of the Xi_c(3123)^+ is seen. We also study properties of the Xi_c(2645)^+ and measure a width of 2.6 +- 0.2 (stat) +- 0.4 (syst) MeV/c^2, which is the first significant determination.