For a given voltage, Ohm's law tells us that if we increase the resistance, then the current must decrease.
But what's actually happening to decrease the current?
If we increase the potential, the current increases, rest all the parameters are constant - which are resistance, material, temperature etc. Drift velocity of the charges, here, have increased due to increased potential.
Drift velocity is $v_d = \frac{e.V.d.\tau}{m}$, where
$e$ - charge
$V$ - Potential
$d$ - distance moved by the charge in time $\tau$
$m$ - mass of the charge
So here we can say that Charges move with greater speed now
Now to change the resistance, let us just change resistivity i.e changing the material and rest all the parameters are same except Free Charge Density of the material, it depends on the material.
Current, $I = n.e.A.v_d$, here $(n.e)$ is the charge density, the effective charge that is flowing per unit volume.
So here the amount freely flowing charge changes and also the drift velocity changes because $\tau$, the effective time between consecutive collisions, may also change.