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We measured transport and noise properties of YBa2Cu3Ox ramp-edge junctions fabricated with interface-engineered barrier. The current-voltage characteristics show a typical resistively-shunted junction like behavior. Voltage noise measurement revealed that the main source of the 1/f noise is the critical current and resistance fluctuations. The analysis of the noise data showed that the critical current fluctuations increase with temperature, whereas the resistance fluctuations are almost constant, and both fluctuations are anti-phase correlated. The magnitudes and the temperature dependence of both fluctuations are found to be sensitive to the junction resistance, which in turn is controllable by the process parameters during the barrier growth.