Is it permissible to take extra money beyond one's needs, under the pretext of studying, without the father's knowledge, to cover personal expenses, given the father's stinginess and refusal to provide money for personal expenditures?

Lying is forbidden by the Qur’an and Sunnah. It is impermissible to lie to one’s father or anyone else. What has been mentioned does not permit lying, especially if the father has fulfilled his basic duties of providing food, drink, clothing, shelter, and education. Thus, it is not permissible to lie to increase study allowance in order to obtain entertainment money. The questioner can inform his mother to speak with the father, and he himself should be gentle with his father, using kind words and showing affection.