I am not really sure what you mean. Do you want to give the high note a "special effect" that is (sounds) different from the rest of the vocal?
If not, I really wouldn't know why you would treat a high vocal note differently from any other vocal note, unless there is a big difference within the dynamic range. You should always control your overall vocals by doing some soft compression (slow attack, fast release). If the high note doesn't fly all over the place your good. just find out which part of the vocal is the loudest (compared to the rest of the vocal track) and compress this part till it sounds roughly the same volume as the rest.
This may help you out:
How to: make a lead vocal sit on top of the mix | MIXINGMAG
Same goes with EQ. The frequency goes up when singing a higher note, but that doesn't mean you should EQ a higher note differently. When placing (EQ) your vocal in the mix you still have a fairly large chunk of the frequency spectrum where your vocal can move around, from at least 100 hz to 12khz+.
If you find that the high note triggers some nasty unwanted frequencies, just find the sweet spot by sweeping your filter and reduce a little it by a small bandwidth / Q.
If you would like to give it a different effect you can go all over the place:"Distortion, extreme compression rates, cabinets, delays, choruses, gating, more extreme reverbs, vocal automations". You name it. There are no rules, just prevent it from clipping and make it sit in the mix by taming it using compression.