The story of Adam and Eve residing in Paradise and their expulsion from there occurs in the Holy Quran. For information about this topic, read the following answers on our website:
"The Sin of Adam and Eve", question 203.
"Angels Prostrating Themselves before Adam as Narrated in the Quran", question 8399.
"Reconciling between Various Reports about the Banned Heavenly Fruit", question 47119.
As for where Adam lived after he was expelled from Paradise, what he ate and how he lived thereupon, there is no report in this regard in the Holy Quran.  Given the fact, that history and historiography cannot help us in this regard, the only source that provides us with some information in this regard is the traditions and sayings of the Infallibles (AS). We will make mention of three narrations which hopefully will clarify the answer to the question. It has been reported from Imam Sadiq (A.S) that he said:
1. After Adam and Eve failed to abide by God's command and they ate from the prohibited fruit, the Lord, the Exalted, said: Get down (leave here), whoever disobeys Me must not be my neighbor in Paradise. That was why, He expelled them from Paradise and gave them abode on earth and left them to provide food and drink by themselves."[1]
2. When Adam fell down to earth, he brought with him one hundred twenty branches and saplings of trees forty of which had fruits which could be eaten both from interior and exterior and forty others could be eaten from interior, not from exterior, and the other forty could be eaten from exterior, not from interior. Also, he carried a woolen bag in which there were grains of those plants."[2]
3. "Verily, when Adam descended from Paradise, he began to have a lot of desire of heavenly fruits. So, God sent down two saplings of grape which he planted. When they grew and bore fruit and the fruits ripened, Iblis came over and built a wall round those vines. Adam said: 'O, the accursed, these do not belong to you. Why did you do that?"
Iblis said: "These trees belong to me."
Adam said: "You are lying."
They started quarrelling until they decided to let the Holy Spirit to mediate between them. Then they told the story to the angel who was close to God (malak muqarrab). The Holy Spirit then picked up a flame of fire which it threw onto the two saplings. The branches of those trees caught fire with Adam and Iblis thinking that trees had burnt completely with nothing left from them. But the fire burnt only two third of the tree and only one third was left unburned. Then the Holy Spirit said: "That much which was burnt was Iblis' share of the tree and that much which was left unburned was Adam's share of it."[3]
It is deduced from all these narrations that Adam and Eve's livelihood on earth was amongst the affairs which they had to tackle personally. As for the fruits referred to in the second and third narration, we must read these two narrations more closely so as to get to an answer.
Considering the second narration which says that the branches which Adam had brought with him from the heavens bore fruit, we cannot say that those fruits were worldly fruits even though he might have eaten some from them after descending. Of course, even if those branches were not fruitful and if they bore fruit after they were planted in earth, again we cannot ascertain which branch bore fruit first and which fruit he ate first.  However, it can be said that the third narration is an explanation of the second narration and it is, therefore, concluded that the first fruit which was grown on earth and which Adam ate in the earth was grapes.

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