<p>Step-edge grain boundary junctions are fabricated using the pulsed laser-deposited YBa₂Cu₃O₇ (YBCO) film on MgO (100) substrates. Steps with height ~ 400&#xa0;nm and angle ~ 20° are obtained using photolithography and ion beam etching (IBE) techniques. Microbridges with varying widths, 2, 5, 10, and 20&#xa0;μm, are fabricated, and their transport properties are studied. A decrease in the critical current and an increase in the normal state resistance of the step-edge junctions are observed with a decrease in the width of the microbridge. The decrease in the <i>I</i>_c is not as sharp as the increase in the <i>R</i>_n value, which leads to the enhanced values of the <i>I</i>_c<i>R</i>_n product at the reduced width of the microbridge. Critical current density value is found to be maximum for the 2 µm wide junction. Also, the scaling behavior of the <i>I</i>_c<i>R</i>_n product with <i>I</i>_c and 1/<i>R</i>_n shows that no change in the transport mechanism occurs with change in width of the microbridge. The behavior of all the junctions is superconductor-normal metal-superconductor (SNS) type, as confirmed by the variation of critical current density with the reduced temperature. The <i>I</i>_c<i>R</i>_n product for the junction with 2 µm wide microbridge obtained at 77&#xa0;K is 0.4&#xa0;mV, which makes it a potential candidate for being used as a terahertz detector.</p>