Lieutenant Joshua Kelly was the ship's engineer aboard the USS Yosemite during the late 2360s.
In 2369, a plasma sample from a plasma streamer exploded in the ship's engine room as a result of quasi-energy microbes. Kelly suffered burns throughout his body and was infected by the microbes along with the rest of the crew. He attempted to remove the microbes using the Yosemite's biofilter, but was unsuccessful and the rest of the crew became trapped in the transporter pattern buffer. Kelly eventually succumbed to ionization in his tissues caused by the microbes.
Soon after, the USS Enterprise-D arrived to find the lost Yosemite. Their away team found Kelly's body, which was taken to the Enterprise-D for autopsy by Doctor Beverly Crusher and Nurse Alyssa Ogawa. (TNG: "Realm of Fear")