If a person is Chayav a Shevu'ah he can be forced to swear on other things that are not Mechayev him a Shevu'ah because of the concept of Gilgul Shevu'ah.
If a person admits that he owes money he is Chayav to pay even if two witnesses testify that he is not Chayav.
If someone denies owing a loan and witnesses testify that he is Chayav he is Kosher for Eidus, but if he denies a Pikadon he is Pasul for Eidus. (1)
The Din of k'Asher Zamam only applies to the testimony of two witnesses. (2)
R. Chiya says if someone claims that his friend owes him 100 Zuz and the friend admits he owes 50 Zuz and immediately offers the 50 Zuz to the claimant he is Chayav a Shevu'as Modeh b'Miktzas.
R. Sheshes holds that if he immediately offers the 50 Zuz he is Patur from a Shevu'as Modeh b'Miktzas because the money that he offers is regarded as if it has already been returned. (3)
If two people are holding a Talis and each one claims that the entire Talis belongs to him the Chachamim decreed that each one shall swear in order to deter a person from grabbing his friend's Talis and claiming it is his.
If a Shtar states that someone owes his friend Sela'im Dinarim without specifying an amount if the lender claims he is owed five while the borrower claims he owes three he is Chayav a Shevu'as Modeh b'Miktzas according to R. Shimon Ben Elazar.
R. Akiva holds he is Patur from a Shevu'ah because he is a Meshiv Aveidah. (4)
If the lender claims that he is owed five and the borrower claims he only owes two everyone agrees he is Patur from a Shevu'ah. (5)
A person doesn't swear for denying a Shibud Karka.
If someone claims that his friend owes him utensils and Karka and his friend admits one and not the other he is Patur from a Shevu'ah.
If he admits partially to the claim on the Karka he is Patur from a Shevu'ah
If he admits partially to the claim on the utensils he is Chayav a Shevu'ah also on the Karka because when a person is Chayav a Shevu'ah on Metaltelin he can be forced to swear also on the Karka because of Gilgul Shevu'ah.
A BIT MORE
1. Someone who denies a loan is Kosher for Eidus because maybe he is simply trying to buy some time because he doesn't have the money, but if someone denies a Pikadon and witnesses testify that the Pikadon was in his house at the time of his denial he is Pasul for Eidus because he is a Gazlan as there is no other explanation why he denied the Pikadon.
2. If one witness testifies and is Mechayev someone a Shevu'ah and his testimony is contradicted by Eidim Zomemim although his testimony is contradicted he doesn't pay ka'Asher Zamam.
3. Since it is regarded as if the 50 Zuz has already been returned he is denying the entire claim and therefore he is Patur from a Shevu'ah.
4. The borrower could very well have claimed he only owes two since the Shtar doesn't specify an amount and thus the implication of the Shtar is that he only owes two and since he admits that he owes three he is a Meshiv Aveidah and the Chachamim decreed that a Meshiv Aveidah doesn't swear because of a Takanas ha'Olam.
5. Because the Shtar implies that he is only Chayav two or because a person is not Chayav a Shevu'ah for swearing on a Shibud Karka.
If a person is Chayav a Shevu'ah he can be forced to swear regarding other things that are not Mechayev him a Shevu'ah because of the concept of Gilgul Shevu'ah. The Nimukei Yosef says that if he is a Chayav a Shevu'ah d'Oraisa Beis Din may force him to swear for other things with a Gilgul Shevu'ah even though his Ba'al Din doesn't make any claim because the concept of Gilgul Shevu'ah is learned out from Sotah that the Kohanim force her to swear that she was not Mezaneh with any other man even though her husband is only claiming that she was Mezaneh with a specific person. However, if he is Chayav a Shevu'ah d'Rabanan it is a Machlokes Amora'im if Beis Din forces him to swear a Gilgul Shevu'ah without his Ba'al Din making a claim.
SHEVU'AS MODEH B'MIKTZAS
If a person admits partially to a claim and he and he says take the amount that I admit that I owe you he is only Chayav a Shevu'as Heses. It is only regarded as a Heilach if the amount that he admits is in his hands in front of Beis Din and he is ready to give it immediately but if he says it is in my house and I will give it to you it is not considered Heilach and he is Chayav a Shevu'ah Shevu'as Modeh b'Miktzas. Even if he gives him a Mashkon on what he admits that he woes hi it is not considered Heilach however according to some opinion is a Mashkon is considered Heilach just as a Shtar is considered Heilach.. (Shulchan Aruch CM 75:6)