Baric nature depends on the tendency of donating the lone pair.

In (I) st amine lone pair of N atom is not in resonance. So it can easily donate the lone pair.

In (II) amine lone pair of N atom is in resonance. So, lone pair is not available.

In (III) amine lone pair of N atom is not in resonance so lone pair can be easily donated.

So, (I) and (III) are more baric compare to (II).

In (I) amine N atom is connected to sp² hybridised carbon atom and in (III) amine N atom is connected to sp³ hybridised carbon atom.

We know sp² carbon atom has more $$-$$ I effect than sp³ carbon atom.

So, in (I) amine density of electrons around N atom will decrease due to $$-$$ I effect and basic nature also decrease.

So, correct order of basic nature : III > I > II