Can a wire having a $610$-$670$ THz (frequency of blue light) AC frequency supply, generate blue light? We know that when we give alternating current across a wire then it will generate an electromagnetic wave which propagates outward.
But if we have a supply which can generate 610 to 670 terahertz of alternating current supply then does the wire generate blue light?
 A: We do have a power supply which can generate current oscillations at optical frequencies: light. It won't transmit any distance along a wire, but if your "current source" and antenna are the same object, you have what is called an optical antenna, and the study of these is an active field of research. I don't know if any of them have any meaningful efficiency down at blue light frequencies, but they do work in the green which is not too far off. See, for example, this review article.
A: It would be hard to generate such a current and harder still to get it to produce any blue light - though this is theoretically possible.
The main problem is that you are probably thinking of a metal wire.  Metals absorb visible light, both reflecting it and turning it into lattice vibrations.  This is because the wavelength of visible light is just a few thousand atoms long in size so it is in a "sweet spot" for exciting solid crystals.  In fact, the tendency for solid objects to absorb, reflect and otherwise interact with visible light is why it is "visible".
In a normal radio wave, your metal wire will need to be on the order of a wavelength of the radio wave you want to produce. This is typically on the order of meters.  Automobiles of the 20th century had metal wires sticking out of them, about 1 meter long, called "antennas", to catch such waves.
But for blue light the wavelength is only about 5 x $10^{-7}$ meters so any useful antenna would be very tiny because an "electron density wave" in your wire would be "turning around" before it got very far.
The electromagnetic spectrum is divided up not so much by "wavelength and frequency" as by the way that any given part of the spectrum interacts with matter.  So, radio waves will interact via electron currents in long metal wires.  But visible light interacts more with lattice vibrations and non-ionizing atomic transitions.  So, "current in a wire" type emission works in frequency up to a thing called "the terahertz gap" https://en.wikipedia.org/wiki/Terahertz_gap .  Above this frequency other emission techniques are usually required.  Blue light is about three orders of magnitude higher in frequency than the terahertz gap.
A: An alternating voltage at that frequency is light. There's no 'generate' about it - the power supply is just a light source.
And if you have a wire, that is, a conductor made of metal, then the light won't propagate inside it at depths longer than the skin depth for that material at that particular frequency, which is generally tiny. 
A: Even at tens of gigaherts, one does not carry current "in" a conductor -- it is carried along the outside (Google "skin effect").
There are transmission lines for high-frequency RF that basically launch an RF wave along a single naked wire, and catch it at the other end -- think of a coax without the outer shield.  If you take this analogy and pursue it into absurdity and beyond, then if you take a really well polished wire, and really carefully launch blue light along its length, then as long as the wire doesn't bend too suddenly, the light -- or some portion of it -- will be refracted and "stick*" to the wire.
I think you could achieve a setup in a lab that involved people looking at a blue-glowing end of a carefully-maintained copper wire or gold wire and going "oooh!".  I doubt there is much potential for practical use here.
* Imprecise language used on purpose -- I'd have to do a lot of work to do the math on this one!
A: I second this Emilio Pisanty's point: the power supply you are
envisioning is a light source. Now the question that remains is: can
you propagate this light through a wire, just like you would do with a
regular low-frequency electric signal?
To get a hint of the answer, look at how people use wires to transport
high frequency signals, into the many MHz up to the multi-GHz range. A
single wire doesn't work, because it has a tendency to radiate all the
power you feed it into the air as free electromagnetic waves. The trick
is to use two wires carrying opposite currents. You can think of them
as one being the signal and the other being the return wire, but their
roles could be symmetric. If you keep them close enough, most of the
electromagnetic field will be confined between them, and you will be
able to transmit the power without too much loses. You can further
reduce the losses by twisting the wires together. At the highest
frequencies, you would get best results by putting one wire inside the
other which, shaped like a tube, functions like a shield. This is called
a coaxial cable, and some of them are good up to tens of GHz.
The think that is not so intuitive is that, while the metal wires carry
the current, the actual power is carried by the electromagnetic field
that propagates between the wires. So the main role of the metal wires
is thus to guide the electromagnetic waves and, for this reason, the
high-frequency cables are considered to be waveguides.
Could you adapt this waveguide technique to the propagation of light?
The answer is yes, some people have indeed built nanosized coaxial
cables for this very purpose.
A: Yeah definitely . You can create light corresponding on any frequency by this method. It’s just that creating this circuit will be very challenging. To give you a perspective, the highest frequency that we have obtained with modern electronic circuits is around 10^11 Hz.
