Nightmare Police

The Nightmare Police (ナイトメアポリス) is a group composed of two Reploids, Bit and Byte, formed by Dr. Doppler to protect Dopple Town.

Mega Man X3
After two Mavericks are defeated, Dr. Doppler sends the Nightmare Police to search and capture X. As a result, the Nightmare Police will now have a chance to appear in empty sub-boss rooms across any of the eight main stages. If the player encounters the Nightmare Police, they must deal with either Bit or Byte. If both aren't defeated with their weaknesses, they will combine into Godkarmachine O Inary in the first Doppler Stage. Additionally, if one is defeated with their weaknesses, but the other isn't, the latter will transform into Godkarmachine O Inary. However, defeating both with their weaknesses will have the player instead fight Press Disposer.

Rockman X3 manga
The Nightmare Police are two Reploids upgraded to have their bodies made entirely of Worms, granting them great power and allowing them to dismantle their bodies and move like Worms. Dr. Doppler only sees them as experiments, having no attachment to them and attacking them alongside X due to them being on his way. As they survived, Doppler decided to use Worms to upgrade them into "a powerful tool", turning them into Godkarmachine O Inary against their will.

Rockman X Giga Mission
Isoc studied Dr. Doppler's works related to the Limited and upgraded it, now calling it the Extreme. He then created two Reploids from data of Doppler's Nightmare Police and the Extreme, Sakitira CC and Pranara DD, and ordered them to search for Zero.