In this paper, some characterizations and properties of right ꬲ-core inverses by using right invertible element and {1, 3ꬲ}-inverse are investigated. Meanwhile, some characterizations for a new generalized right ꬲ-core inverse which is called right pseudo ꬲ-core inverse are also studied. The relationship between right pseudo ꬲ-core inverses and right ꬲ-core inverses are presented.