Across a metallic conductor of non-uniform cross section a constant potential difference is applied. The quantity which remains constant along the conductor is

As there is no accumulation of charges, the current through the conductor will be constant at every cross-section.
$J=\frac{I}{A}\mathrm{\&}{v}_d=\frac{1}{neA}$
As cross-sectional area is changing, current density and drift velocity will change. For a length element dl,
$dV=i\left(dR\right),dR=\frac{\rho \left(dl\right)}{A},E=\left|\frac{dV}{dl}\right|$
As area is varying, resistance will vary, due to which potential difference across the element will vary. Hence, the electric field will vary across the length.