What is the ruling on one who began fasting Ramadan while in disagreement with his parents over household expenses, which he bears alone without fair participation from them, despite their ability to help?

You must strive to please your parents and spend on them, even if it is beyond your capacity, while seeking reward from Allah. It is not reprehensible to be sensitive about their requests for money for sustenance, unless it is for something forbidden. You can speak with them kindly about your needs and your inability to provide more. The month of Ramadan is an opportunity to mend what is between you and your parents, and spending on family is among the best forms of charity in terms of reward.