Two-dimensional (2D) transition metal chalcogenides (TMCs) become more attractive upon addition of a third element owing to their unique structure and remarkable physical and chemical properties, which endow these materials with considerable potential for applications in nanoscale devices. In this work, a RexNb(1-x)S2-based saturable absorber (SA) device for ultrafast photonics applications is studied. The device is assembled by placing RexNb(1-x)S2 nanosheets with a thickness of 1-3 nm onto a microfiber to increase their compatibility with an all-fiber laser cavity. The prepared RexNb(1-x)S2-based device exhibits a modulation depth of 24.3%, a saturation intensity of 10.1 MW/cm2, and a nonsaturable loss of 28.5%. Furthermore, the RexNb(1-x)S2-based device is used to generate ultrashort pulses in an erbium-doped fiber (EDF) laser cavity. At a pump power of 260 mW, the EDF laser operates in a conventional soliton mode-locked region. The pulse width is 285 fs, and the repetition frequency is 61.993 MHz. In particular, the bound-state soliton mode-locking operation is successfully obtained in a pump power range of 300-900 mW. The bound-state pulses are formed by doubling identical solitons with a temporal interval of 0.8 ps. The output power is as high as 47.9 mW, and the repetition frequency is 123.61 MHz. These results indicate that the proposed RexNb(1-x)S2-based SAs have comparable properties to currently used 2D SAs and provide a basis for their application in the field of ultrafast photonics.