I use a simple N channel J-Fet with the gate connected to GND. I used to use J110, J111, J112, J113, each having a different v-gs giving a different voltage output. From Jfet-Jfet, the voltage varies a bit, but, each Jfet will act as a linear regulator and hold their voltage.
(I once went through all the available J-Fets at Digikey, I had a selection of output voltages from 2.1v to 5.4v. Sorry, I no longer have that table list of part numbers VS output voltage.)
The input is the drain and the output is the source. The maximum input voltage is what the Jfet can handle. The minimum input voltage is the actual output voltage, (in other words, 0v dropout regulator), otherwise the output voltage = the input voltage anywhere below that point.
The quiescent current to GND is in the low Fento-Amp range, in other words, nothing. Perfect for projects needing regulation with small watch battery lithium cells. Even the smallest batteries would last over a decade with no drain at all. Note that if you want low Fento-Amp currents, the quality of flux residue cleaning on you PCB now counts, you'll waste current if it is not done really good!
If you need to supply more than 25ma, feed the output of this regulator into an NPN transistor's base in an emitter-follower configuration, or, Vgs match a few Jfets and tie them all in parallel.
Now for your application. Based on your description, 'I think', what you mean to do is use the same Jfet as above, but have a cap with bias correcting battery in series to the gate. Your source load would be on the other side of that cap. However, this will have no gain, and there may be a fixed offser error on the output, but, the in to out would have close to nothing in current. And depending on the cap, ony offset charge will hold very long. However, any build of charge in that cap beyond the Jfet's capabilities may destroy the Jfet, so you have a narrow operating range. (The capacitor is your 2 plates) Use the output of the Jfet to feed your opposite plate directly, or, take that output and feed a standard op-amp to invert that signal to make that repelling voltage.
Your other choice is to look for Fento-amp-input op-amps and use 1 as a voltage follower, then feed another op-amp in an inverter configuration which then feeds your capacitive plate.