What kind of transistor turns on with 0.2 volts?
Whilst I'm inclined to agree with @Bimpelrekkie that this is probably an X-Y problem, for those who might actually need such a device there are some options. Most MOSFETs are sold as enhancement or depletion mode (less commonly) devices, however it's possible to tune the threshold voltage to approximately zero +/- tens of mV. 

For example, the Advanced Linear Devices ALD110800A and similar devices in that series have a nominal zero gate threshold (1uA Ids). The subthreshold behavior is fairly well documented as well. 



For your actual situation, use CrossRoads circuit with just about any single supply op-amp or single-supply comparator. LM358 or LM393 will work fine from a 5V supply.