Am I obligated to pay a sum of money to the institute from which I withdrew due to abuse and injustice, knowing that I did not complete my studies there and did not receive any certificate or proof?

If the amount is a due fee for past studies, then it is not permissible to withhold payment, because the tenant has benefited from the service. This falls under the warning mentioned in the Hadith: "There are three whose adversary I shall be on the Day of Resurrection: a man who gave by My Name and then betrayed; a man who sold a free person and consumed his price; and a man who hired a laborer, benefited from his work, and did not give him his wages." If the amount is for a period not yet studied, and the reason for discontinuing studies is the oppression and hardship imposed by the institute, then it is permissible to terminate the contract due to harm, after it has been proven and estimated by experts. In this case, there is no obligation to pay the fee for the future period unless they remove the harm.