Is it permissible to pay the fidyah instead of fasting in Ramadan due to strenuous work and debts, knowing that not fasting might be a sin?

Fasting in Ramadan is obligatory, and the fidyah (ransom) does not substitute for fasting. If completing the fast during the day becomes an unbearable hardship, then breaking the fast is permissible, with the obligation to make up the missed days after Ramadan.