Steady current flows in a metallic conductor of non-uniform cross-section. The quantity/ quantities constant along the length of the conductor is/are

If E be electric field, then current density $j=\sigma E$ Also we know that current density  $j=\frac{i}{A}$Hence j is  different for different area of cross-sections. When j is different, then E is also different. Thus E is not constant.

The drift velocity  $v_d$ is given by $v_d=\frac{j}{ne}=$different for different j values. Hence only current i will be constant.