Relativistic millicharged particles (chi(q)) have been proposed in various extensions to the standard model of particle physics. We consider the scenarios where they are produced at nuclear reactor core and via interactions of cosmic rays with the Earth's atmosphere. Millicharged particles could also be candidates for dark matter and become relativistic through acceleration by supernova explosion shock waves. The atomic ionization cross section of chi(q) with matter are derived with the equivalent photon approximation. Smoking-gun signatures with significant enhancement in the differential cross section are identified. New limits on the mass and charge of chi(q) are derived, using data taken with a point-contact germanium detector with 500 g mass functioning at an energy threshold of 300 eV at the Kuo-Sheng Reactor Neutrino Laboratory.