Consider a conductor of metal with non-uniform cross-section. The parameter that is constant is: 

Concept:

The amount of current travelling per unit cross-section area is known as current density and expressed in amperes per square metre.

Formula for current density is \(J=\frac{I}{A}\)

1. When a steady current flows through a non-uniform cross-sectional metallic conductor, the current flowing through the conductor is constant.
2. Since the current is independent of the conductor area, it remains constant.

The explanation for the incorrect options:

1. Current density, drift velocity and drift speed are all inversely proportional to cross-sectional area.
2. These quantities are not constant along the length of the conductor.

When a steady current flows in a metallic conductor of non-uniform cross-section then the drift speed is \(v_d=\frac{I}{neA}\)  and the current density \(J=\frac{I}{A}\)
⇒\(v_d\propto\frac{1}{A},\ J\propto\frac{1}{A}\)
⇒ Only current remains constant.

In a metallic conductor of non-uniform cross-section, only the current remains constant along the entire length of the conductor.

Hence, the correct answer is Option-3-current.