Is it permissible for a student to use the internet to seek Islamic knowledge, despite the objection of his father who pays the subscription fees and who does not explicitly forbid him from seeking knowledge but expresses his discomfort with it?

We advise you to continue and strive diligently in seeking knowledge, with sincere intention for Allah therein and seeking His help, for the purpose of knowledge is to act upon it and draw closer to Allah. Beneficial knowledge increases its possessor in dutifulness and kindness to his parents. Explain the virtue of knowledge to your father in a good manner. Turn away from the whispers of Satan that deter you from seeking knowledge, for your use of your father's internet in seeking knowledge is permissible. We also advise you to continuously read books on the etiquette of seeking knowledge, such as the book Jami' Bayan al-'Ilm wa Fadlihi by Ibn Abd al-Barr.