Concept of Sadiqa Jariyah (Continuing Charity after death) came from the Hadiths.
Here is a hadith attributed to Prophet Muhammad after his death.
Abu Hurairah (May Allah be pleased with him) reported:
The Messenger of Allah said, “When a man dies, his deeds come to an end except for three things: Sadaqah Jariyah (ceaseless charity); a knowledge which is beneficial, or a virtuous decendant who prays for him (for the deceased).”
Book 13, Hadith 1383
The verse usually quoted by Hadith followers to support the Concept of Sadiqa Jariyah is 36:12.
When you try to understand this verse then you will notice the word “Atharahum” is not referring to the concept of Sadiqa Jariyah but something else.
Let us check the verse 36:12,
36:12 It is indeed Us who resurrect the dead, and We record what they have done and their footsteps (Atharahum). And everything We have counted in a clear ledger.
It means God recorded the deeds of the dead people and recording the deeds of those who are following their footsteps.
The book of deeds which will be displayed on judgment day will contain the good deeds and bad deeds 17:13 & 18:49. The good deeds means how many times we obeyed God and bad deeds means how many times we disobeyed God.
According to my understanding the Book of deeds of a person closes down with his/her death.
17:13 And We have attached to the neck of every human being his deeds, and We bring forth for him a record on the Day of Resurrection which he will find on display.
So nowhere we are commanded to
1-Hire a person to do hajj on one’s behalf.
2-Perform Hajj on behalf of deceased parents.
3-Pay Zakat on behalf of the deceased.
4- Perform Obligatory Fast on behalf of the deceased.
5-Sacrifice an animal on behalf of the deceased.
6-Pay Charity (Sadaqa) on behalf of the deceased.
PEOPLE WHO ARE DEAD ARE NATION WHICH PASSED AWAY
2:134 That is a nation that has passed away; to them is what they have earned, and to you is what you have earned; and you will not be asked regarding what they did.
2:141 That is a nation that has passed away; to them is what they have earned, and to you is what you have earned; and you will not be asked regarding what they did.
EVERY SOUL WILL BE PAID WHAT IT HAS EARNED
2:281 And be aware of a Day when you will be returned to God then every soul will be paid what it has earned, and they will not be wronged.
3:25 How shall it be when We gather them on the Day in which there is no doubt; and every soul shall receive what it has earned, and they will not be wronged.
4:51 Thus God will recompense every soul for what it had earned. God is swift in reckoning
NO BEARER MAY CARRY THE BURDEN OF ANOTHER
6:164 Say: “Shall I seek other than God as a Lord when He is the Lord of everything?” And every soul earns what is for it; and no bearer may carry the burden of another. Then to your Lord is your return and He will inform you of what you disputed in.
16:25 They will carry their burdens in full on the Day of Resurrection, and also from the burdens of those whom they misguided without knowledge. Miserable indeed is their burden.
17:15 Whoever is guided is guided for himself, and whoever is misguided is for his own loss. And no bearer may carry the burden of another; and We were not to punish until We send a messenger.
39:7 If you reject, then know that God is in no need of you, and He is displeased with rejection for His servants. And if you are thankful, He is pleased with it for you. And none shall carry the burdens of another. Then to your Lord is your return, and He will inform you of everything you had done. He is fully aware of what is in the chests.
53:38 None can carry the burdens of another.
74:38 Every soul is held by what it earned.