The Ansata dimensional shifter device.
The Sikarian spatial trajector module.
Folded-space transport is a form of dimensional shifting that can be used in place of the transporter to move objects from one location to another. Folded-space transport was first proposed in the Elway Theorem but it was discarded by the mid-22nd century.
The dimensional shifting involved in folded-space transport proved dangerous to humanoid tissue and long-term use of the method was fatal. Nonetheless, the Ansata separatist movement of Rutia IV had developed a form of the technology powered by an Inverter and by 2366 the more committed members of the group used the device frequently in their terrorist campaign on that planet.
Folded-space transport was extremely effective for the Ansata because it was not traceable by any standard scanners and could not be blocked by force-fields or other barriers. This allowed the Ansata to materialize within the boundaries of their target area and vanish again without any fear of being trapped or tracked. (TNG: "The High Ground")
The only other known example of working folded-space transport was the spatial trajector employed by the Sikarians who were encountered in 2371, by the USS Voyager. The Sikarian device had a range of over 40,000 lightyears.
Voyager considered utilizing the technology but ultimately realised that it was incompatible with that of the Federation. (VOY: "Prime Factors")