What is the ruling of Islamic law on cooking and distributing food every Thursday for the soul of the deceased, and is this permissible or an innovation (bid'ah)?

Donating food on behalf of the deceased and distributing it to the needy, without gathering at the deceased's home, has no religious prohibition. Designating Thursday for this is permissible if the intention is to seek out the Thursday on which deeds are presented to Allah the Almighty, based on the Prophet's (peace be upon him) saying: "Deeds are presented on Mondays and Thursdays, and I love for my deeds to be presented while I am fasting."