Unless you have the mental fortitude to just not scratch your mosquito bites, the most effective way to stop them from itching, according to scientific evidence, is with antihistamines.
When a female mosquito bites you (the bugs use your blood to grow eggs, so the males have no reason to bite), it injects its saliva under your skin.
The saliva contains anticoagulants that make your blood easier to slurp up.