Is it permissible to travel to study at the Islamic University of Madinah without the consent of the father, who fears the consequences of that on residency in the United States of America, given the mother's consent?

Seeking knowledge is of two types: obligatory (wajib) and voluntary (tatawwu'). A son may travel to seek obligatory knowledge without his parents' permission if he cannot acquire it in his own country, similar to Hajj and Jihad when they become obligatory. As for non-obligatory knowledge, he may not travel without their permission. There is no obedience to parents in disobedience to Allah. Today, obligatory knowledge can be acquired without travel through books, the internet, and scholars. Therefore, do not travel for study except with your parents' permission, strive to convince your father, and seek help from those who are trustworthy.