The answer to your question is yes and no.
If you are using UVA light (black light) then this is safe for your fish; most of the light sources used on fish tanks do emit these wavelengths to some degree, but the black light sources are coated with a material that filters out the other wavelengths from red to blue light so it radiates only near ultraviolet and infrared light (heat).
The dangerous types of ultraviolet light are UVB and UVC; UVB is what gives you a tan or a sunburn, while UVC is the most dangerous type of ultraviolet light - this is used to kill bacteria and algae in water and to sterilize surgical equipment, among lots of other uses.
UVC radiated from the Sun is stopped by the atmosphere so it does not reach the ground, but it can be measured in Antarctica due to the ozone hole there.
More information could be found in this Wikipedia article about ultraviolet light.
Near UV = UVA.
Middle UV = UVB.
Far UV = UVC.