Accurate manipulation of a substance on the nanoscale and ultimately down to the level of a single atom or molecule is an ongoing subject of frontier research. Herein, we show that topologies of water monolayers on substrates, in the complete wetting condition, can be manipulated into rich forms of ordered structures via electrowetting. Notably, two new topologies of monolayer ices were identified from our molecular dynamics simulations: one stable below room temperature and the other one having the ability to be stable at room temperature. Moreover, the wettability of the substrate can be tuned from superhydrophobic to superhydrophilic by uniformly changing the charge of each atomic site of the dipole or quadrupole distributed in an orderly manner on the model substrate. At a certain threshold value of the atomic charge, water droplets on the substrate can spread out spontaneously, achieving a complete electrowetting. Importantly, unlike the conventional electrowetting, which involves application of a uniform external electric field, we proposed non-conventional electrowetting, for the first time, by invoking the electric field of dipoles and quadrupoles embedded in the substrate. Moreover, different topologies of water monolayers can be achieved by using the non-conventional electrowetting. A major advantage of the non-conventional electrowetting is that the contact-angle saturation, a long-standing and known limitation in the field of electrowetting, can be overcome by tuning uniformly the lattice atomic charge at the surface, thereby offering a new way to mitigate the contact-angle saturation for various electrowetting applications.