I’ve been told by different people that if you have a fresh mosquito bite, that if you use your fingernail to mark an X in the middle of the bite that this will cause it to be less irritating and it will heal faster.
I suppose the idea is that you forcing the poison/irritant/whatever you want to call it into quadrants and it is less concentrated in one area, resulting in less of a welt and less itching.
I’ve tried it, and it seems that it may help somewhat, but it may all be in my imagination.
I discovered that this works when I was a kid, except I put four deep indentations in a bite with my thumbnail rather than two. I always thought it worked because it makes my skin hurt (I press my thumbnail down HARD!) so much I forget it itches! 
Yes, it works, but not because of “quadrants.” It’s sensory overload. You’re dialing in so much discomfort that the nerve won’t talk anymore. You can do the same thing by smacking it with a flyswatter or a chopstick; or by scratching. Scratching, though, tears up the skin, so you don’t want to do that.
If you’re not into such natural cures, there’s always hydrocortisone cream.
If you don’t have hydrocortizone cream around, trying just plain old underarm deoderant or anti-perspirant. I got that tip from a doctor’s wife. It works for me!
If you don’t scratch the bite it will be gone on it’s own within 24 hours. Can’t take the itching?
Hot water. Just don’t burn yourself.