What is the ruling on being absent one day per week and submitting a leave request for it to be deducted from annual leave, knowing that the deputizing authority deducts all incentives if the days of absence exceed the allowed monthly limit?

You must inform the delegating authority of your family circumstances. If they agree to continue granting you incentives despite your leave exceeding the allowed limit, then that is well and good. Otherwise, it is not permissible to resort to deception to continue receiving incentives, for the Messenger of Allah, peace and blessings be upon him, said: "Whoever cheats is not one of us," and "Muslims are bound by their conditions concerning what is permissible." You are entitled to claim payment for overtime hours.