• “I have to study” => Je dois étudier. or J’ai à étudier.
• “I need to study” => J’ai besoin d’étudier.

“Je avoir à étude” corresponds to nothing¹ (2 errors); “je” is a personal pronoun, therefore there must be a conjugated verb form after it, never an infinitive.
It is apparent that the verb in question is “avoir” when its sens is “have to”; “to” is rendered by “à”, but just as in English that must be followed by an infinitive, never a noun: “I have to go. => J’ai à m’en aller.”.

¹_{More exactly, it is meaningless}

In addition to je dois étudier, another common and idiomatic way to say it is :

Il faut que j’étudie.

Additionally,

J’ai besoin d’étudier

is also common, but maybe less so.

Je avoir a etude

is plain unintelligible. A better phrase would be

Je dois étudier

as others have stated.

“Apprendre” can sometimes be substituted here, as long as “to learn” would be equivalent.