What is the ruling of the Shari'ah on marriage by intention, knowing that the couple established a marital relationship without a contract, with the knowledge of their families and neighbors about this relationship?

Marriage is a great ritual, and it is not permissible to make it a means of achieving cheap ends. If the marriage fulfills the legitimate conditions and pillars (presence of a guardian, two just witnesses, a contract formula), then it is valid, and the purpose of obtaining citizenship does not affect its validity. However, if it is merely a marriage on paper without the legitimate conditions, then it is not a marriage and cohabitation in it is fornication. We did not understand what is meant by marriage with intention, but if what is meant by it is cohabitation without a legitimate contract with a guardian and witnesses, then it is fornication. You have done well by repenting, and it is obligatory to cut off this relationship. If you wish to enter into a legitimate marriage, there is no harm after purification with three menstrual cycles, or one menstrual cycle according to some scholars.