Is there ONE essential oil that will keep away the sting of the dreaded mosquito? The short answer is no. But using a combination of essential oils that have been shown historically through time to be effective deterrents will definitely help in keeping you safe from the bite and possible exposure to harmful mosquito born illnesses like Zika, Dengue and others.
While DEET is the best known synthetic applicant for mosquito repellents and one which is still recommended by the CDC for use in protecting from mosquito bites, the prolonged use of it can be dangerous as it accumulates in the body. The jury is still out on its long term use and safety to the human body, but there are other natural deterrents that if used correctly, can be as effective at being a deterrent for the dreaded mosquito. Recent studies have shown where the oil of Lemon Eucalyptus has been extremely effective in keeping the mosquitoes at bay. Will it outright prevent a mosquito bite, not alone, but combined with other essential oils that have historical uses for deterring mosquito bites, Lemon Eucalyptus essential oil becomes extremely effective.
“One of the earliest studies on eucalyptus essential oil as an insect repellant was in 1996. The study was conducted in Bolivia and showed that a eucalyptus-based insect repellant was able to protect the skin from Anopheles mosquito bites from 6 to 7.75 hours. The females of the genus Anopheles is responsible transmitting malaria. 
A study published in 2012 focused on Aedes egypti, the kind of mosquito that is responsible for dengue fever. Dengue fever is characterized by sudden onset of fever, joint pain, and in worst cases, massive bleeding. Essential oils from a variety of eucalyptus plants were found to have fumigant and adulticidal and larvicidal characteristics. 
The primary ingredient in most commercial insect repellants is DEET, which stands for diethlytoluamide.
DEET remains the standard by which all other repellents are judged and products range in strength from 10% to 100%, though over 50% concentration should not be used on skin. 
A 2002 study compared eucalyptus with DEET and the Eucalyptus scored 96.89 percent effectiveness, compared to DEET’s 84.81 percent against Anopheles (Malaria carrying) mosquitoes. Similarly, a more recent 2014 study revealed how lemon eucalyptus oil is as effective as DEET, greater than with a 32% solution of Lemon Eucalyptus Oil scoring 95 percent effectiveness – compared to a 40% solution of DEET’s 100 percent. 
Another mosquito-borne disease is Filariasis, which is caused by Culex mosquitoes. Filariasis causes blockages in the body’s lymphatic system, leading to the enlargement of different body parts. The results of a June 2014 study concluded that the nanoemulsification of eucalyptus oil has larvicidal activity against the Culex genus.”  http://www.herbs-info.com/blog/study-finds-lemon-eucalyptus-essential-oil-is-better-mosquito-repellent-than-deet/
My suggestion in searching or even in creating a natural, safer alternative to the synthetics out there to deter mosquito bites are to look for products that contain most of, if not all of the following essential oils you will find in this link from American College of Healthcare Sciences. Creating your own natural insect deterrent can be fun and have wonderful results. And you can feel confident in knowing that you are protecting yourself and loved ones by using something that is good for you and the environment.