Careful English speakers will not say an because it is definitely incorrect. The only way to say it is a university, since this particular word actually begins with a consonant sound. It doesn't matter whether the word is written with a vowel or consonant, but whether it is pronounced with a vowel or a consonant.In fluent everyday speech I would say a university. One could reason that there is an invisible "yoo" at the beginning of the English pronunciation, hence the word does not sound as if it begins with the vowel "u" (pronounced "oo") but with the consonant "y" pronounced "yoo". Very careful English speakers might say "an"; certainly you will find both in written English: with a and an.
I want to say: "The land is going to be used for the construction of a technical institute and a university". Is it correct to say a university or an university?