Dear sheikh if someone claims an item found with somebody else and brings forward his evidence and proof and the other party denies the claims and he swear an oath on it. In whose favour will the case be decided.since we have witness vs oath at the same time.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If two people dispute over the ownership of something which is already in the possession of one of them, then in principle it is ruled that it belongs to the one in whose possession that thing is now (i.e. if the other person has no evidence to prove his claim). If he takes an oath that it is his, it is ruled that it belongs to him because the presumption is that if someone has something in his possession, it is ruled that he is its owner.

The Fiqh Encyclopedia reads: "Possession as evidence of ownership: The jurists have agreed in general that having something in one's possession is evidence of owning it, and they have elaborated beyond that." [End of quote]

Kash-shaaf Al-Qinaa‘ reads: "If two people claim to own something, then it is one of the three following cases: One of them is if the item is in the possession of one of them only: it belongs to him if he takes an oath that he owns it, and the claimant has no right to it if he has no evidence to prove his claim; the Prophet, sallallaahu ‘alayhi wa sallam, said in the story of the Hadhrami (man from Hadharamawt) and the Kindi (man from Kindah): 'Your two witnesses or his oath; there is nothing else that can be considered in this regard.' This is because if someone has something in his possession, he is evidently the owner." [End of quote]

If the other person brings forth legitimate evidence that the item is his property, then it will be ruled in his favor, and the oath of the one in whose possession it is, is annulled and his denial or oath is of no avail, as Ibn Abbaas narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: "If people were to be given according to their claims, some men would claim the blood and property of others, but an oath is required of the one who denies (the claim)." [Al-Bukhari and Muslim]

Another narration by Al-Bayhaqi with a good chain of narrators reads: "…the burden of proof rests upon the claimant and the oath rests upon the one who denies (the claim)."

As-San‘aani said in Subul As-Salaam: "The Hadeeth is evidence that no statement of any person is accepted in what he claims just by claiming it, but he needs to provide evidence, or the defendant is believed.”

The least amount of evidence considered in property claims is the testimony of one man and two women. As regards the testimony of one man along with the oath of the claimant, there is a difference of opinion about its acceptance as evidence; the correct opinion is that it is accepted as evidence, as Ibn ‘Abbaas said that the Prophet, sallallaahu ‘alayhi wa sallam, judged (between two people) with an oath and one witness. [Muslim and Ahmad]

Ibn Qudaamah said in Al-Mughni: "The least (amount of evidence) than can be accepted in property cases is a man and two women, or a trustworthy man along with the oath of the claimant … and most scholars are of the view that a property claim is valid with a witness and an oath; this has been reported from Abu Bakr, ‘Umar, ‘Uthmaan, and ‘Ali . This is also the view of the seven jurists and ‘Umar ibn ‘Abdul-‘Azeez, Al-Hasan, Shurayh, Iyaas, ‘Abdullaah ibn ‘Utbah, Abu Salamah ibn Abdur-Rahmaan, Yahya ibn Ya‘mur, Rabee‘ah, Maalik, Ibn Abi Layla, Abu Az-Zinaad and Ash-Shaafi‘i. But Ash-Sha‘bi, An-Nakha‘i and the scholars of the Hanafi School, and Al-Awzaa‘i said: the case will not be judged with a witness and an oath only." [Summarized]

Therefore, in this case, the ruling will be in favor of the claimant with the evidence that he has, which is a witness and an oath, or two witnesses.

Allaah Knows best.