שמות פרק כב, ח עַל-כָל-דְׁ בַר-פֶּשַע עַל-שוֹר עַל-חֲמוֹר עַל -שֶּה עַל-שַלְׁמָה עַל -כָל-אֲבֵדָה אֲשֶּר יֹאמַר כִי-הוּא זֶּה
מסכת בבא קמא דף קז/א אמר רב חייא בר יוסף עירוב פרשיות כתוב כאן וכי כתיב כי הוא זה אמלוה הוא
The concept of Modeh B’Miktzas is admitting to a portion and being exempt from paying the balance with an oath. כי הוא זה implies “this” and no more, and thus, one admits to only a portion of the claim. The context of the verse is concerning one who is accused of stealing, yet the verse is concerned with disputes regarding loans and their repayment. The law of swearing on the denied balance only applies in disputes involving loans or deposited items. Further, if a person denies the whole requested amount of the loan, then according to Torah law one does not take an oath. The reasoning being that one is not brazen enough to completely deny a loan to the person that was kind enough to provide to the loan to him; but one would admit a part, thinking to pay back the balance later. This reasoning would not apply to the case of deposits since the defendant did not receive a chesed. This is the opinion of Rashi (but Tosefos disagrees).
Further note that this only applies when one admits on their own. However, if witnesses testify about loan, then this is not considered admitting by oneself. This is implied from the verse as well.
Further derived from the verse is that if one offers, in place of admitting, a payment of a portion and denies the rest, this is also not a case of Modeh B’Miktzas. In this case, the two portions are considered separate: one is being paid back, and the other portion becomes a separate loan with complete denial. The verse says “one will say” would be obligated and not that “one will give”.
