Is it possible to manipulate some specific atoms of a liquid metal by dint of the magnetic field, electric field, etc?
While Field Structured Composites are a thing, they use nano- to micro-scale particles in a polymer matrix, with particle alignment controlled/influenced by applying electric or magnetic fields during curing.
Trying to do this at the atomic level, as you ask about above, runs into several problems. These include:

Overcoming the desire of the liquid to mix, so you need your desired element to have a fairly well tuned positive heat of mixing to just balance the entropic contributions to the free energy. Or, in other words, just barely soluble.

Overcoming diffusion in the liquid would require strong interactions of your field with the specific element (and only that element). This runs up against the limits below.

In a metallic liquid, applying an electric field isn't going to specifically target any one atom type since the free electrons will shield the bulk from the field. Ions in a dielectric liquid would be a better choice (much like the field structure composites above), but that is just the reinvention of ion chromatography.

The magnetic moments of atoms are pretty darned small, so you won't get the ferromagnetic boost that can be achieved with particles. Applied magnetic fields will have to be enormous if they would even work at all.