My first guess is a bad contact between a probe and a sample. Or is this effect observed every time you mount the sample? Anyway, be careful because sparking is not healthy for the probe.
In the 4-point probe measurement, a current is pushed between the outer probes and the voltage drop is measured between the inner probes. So, By trying to pass the specified current the voltage increases as you have bad contact such that you have an air gap between the prove tips and the specimen.
So, you have to make good contact,
you set the probes before injecting the current
You reduce the measuring current to minimum.
If sample is fragile you can contact it with four spots of silver epoxy supplied with 4 fine wires that may be attached to a pcb pads. From the pcb pads you can easily access the specimen.