Some people have told me adoption is not allowed in Islam, but i could not find any hadees or verses to be sure of this thing. Is it true?
The confusion arises because of different meanings of the word "adoption" in English and it's perceived equivalent in Arabic. In Arabic, in addition to taking an orphan in and feeding them and providing for them and raising them (this is kafalah), it also means to give them your name and have them inherit from you and have similar mahram rules apply to them as with one's own children (this is tabanna). It is the second part of the above that Allah SWT forbade in the Qur'an when He said in Surat al-Ahzab:4:
“…nor has He made your adopted sons your real sons…”
In a hadith in Sahih al-Bukhari and Sahih Muslim, Abu Dharr al-Ghifari (ra) narrates that the Prophet (saws) said that there is no man who knowingly calls himself after someone other than his real father, except that he has committed kufr.
Sponsoring an orphan, however, (by which one means bringing an orphan to live in one's house, or taking care of their expenses in another location) and raising them occupies a very high status in Islam and is the cause of a great reward from Allah. The Companion Sahl b. Sa'd (ra) narrates in Sahih al-Bukhari that the Prophet (saws) said he and the one who sponsors an orphan will be like so in Paradise, and he made a gesture with his index and middle fingers holding them very close to each other, just slightly apart, indicating closeness. The Prophet (saws) practice was to look after orphans and care about them and have concern for them. There are numerous ayaat in the Qur'an about treating orphans well and dealing justly with them and their property.
And the best example is the Prophet (saws) with Zaid b. Haritha (ra) - he loved him like his own son. The narrations that we have about how they interacted with each other are simply beautiful - in fact the Companions said they had no idea he wasn't the Prophet's (saws) real son until Zaid's biological family showed up (and he didn't want to go with them even when the Prophet (saws) gave him the choice!).
ادْعُوهُمْ لِآبَائِهِمْ هُوَ أَقْسَطُ عِندَ اللَّهِ فَإِن لَّمْ تَعْلَمُوا آبَاءهُمْ فَإِخْوَانُكُمْ فِي الدِّينِ وَمَوَالِيكُمْ وَلَيْسَ عَلَيْكُمْ جُنَاحٌ فِيمَا أَخْطَأْتُم بِهِ وَلَكِن مَّا تَعَمَّدَتْ قُلُوبُكُمْ وَكَانَ اللَّهُ غَفُورًا رَّحِيمًا
Call them by [the names of] their fathers; it is more just in the sight of Allah . But if you do not know their fathers - then they are [still] your brothers in religion and those entrusted to you. And there is no blame upon you for that in which you have erred but [only for] what your hearts intended. And ever is Allah Forgiving and Merciful.
Ahzab 5 (33/5)
Adaption is OK. But you cannot claim that you are the father of the child you adapted.