Okay, so you've got a transimpedance amplifier (inverting) so there's a virtual ground at the inverting input. That virtual ground might be a few mV one way or the other from actual ground, depending on the Vos. If it's a true current input you'll just see the same offset at the output. You can subtract the offset after the amplifier or do this:
You'll need two suitably(do the math) stable references (plus and minus). Say you have +/-2.5V and you want to be able to adjust the offset by +/-5mV. You can connect a pot across the references (so +/- 2.5V appears at the wiper) then divide that down appropriately say with 100K and 200 ohms (100K should be much less than the pot element resistance) , then apply that voltage to the non-inverting input. If the offset is entirely due to the internal offset of the op-amp the virtual ground will then be exactly 0v when the output is adjusted to 0mV (assuming negligible bias current).
By the way, the offset adjust terminals on an op-amp (where available) should not be used to compensate for offsets that are external to the op-amp, as the are not derived from a reference, the voltage will tend to be something like proportional to absolute temperature (not very stable).