Born in the northern city of Trujillo, La Libertad, Quesada was raised in Huanta, Ayacucho. From a very young age, he registered himself in the Peruvian Aprista Party. After finishing his high school education at María Auxiliadora Grand School Unity in 1981, he travelled to Lima in order enroll in the Universidad de San Martín de Porres to study law. He was able to finish his law degree in 1996.