In the situation described, if your mother is fully incapable of fasting due to old age or severe illness, and she has no hope of regaining her health and the ability to fast, you can give fidyah for her missed fasts.
However, if she does somehow regain her health and the ability to fast later on, it will become obligatory for her to perform qaza for the missed fasts, despite the fact that you have already given fidyah.
The amount to be given as fidyah for one fast is equal to the amount given for sadqa al fitr which is 1.75 kg of wheat or money equivalent to the price of 1.75 kg of wheat.
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دلائل:
الدر المختار مع رد المحتار: (427/2، ط: دار الفکر)
(ویفدی) وجوبا ولو فی اول الشھر وبلا تعدد فقیر کالفطرۃ لو مؤسرا۔
(قولہ للشیخ الفانی)ای الذی فنیت قوتہ أواشرف علی الفناء ولذا عرفوہ بانہ الذی کل یوم فی نقص الی ان یموت نھر۔ومثلہ مافی القھستانی عن الکرمانی: المریض اذاتحقق الیأس من الصحۃ فعلیہ الفدیۃ لکل یوم من المرض۔۔۔
(قولہ العاجزعن الصوم)ای عجزا مستمرا کما یأتی۔
Allah the Almighty knows best.
Darul ifta Al-Ikhlas, Karachi.