On the authority of Ibn Abbas (may Allah be pleased with him), that the Messenger of Allah ﷺ said:

Were people to be given everything that they claimed, men would [unjustly] claim the wealth and lives of [other] people. But, the onus of proof is upon the claimant, and the taking of an oath is upon him who denies.

A hasan hadeeth narrated by al-Baihaqee and others in this form, and part of it is in the two Saheehs.

عَنْ ابْنِ عَبَّاسٍ رَضِيَ اللَّهُ عَنْهُمَا أَنَّ رَسُولَ اللَّهِ ﷺ قَالَ: "لَوْ يُعْطَى النَّاسُ بِدَعْوَاهُمْ لَادَّعَى رِجَالٌ أَمْوَالَ قَوْمٍ وَدِمَاءَهُمْ، لَكِنَّ الْبَيِّنَةَ عَلَى الْمُدَّعِي، وَالْيَمِينَ عَلَى مَنْ أَنْكَرَ" .
حَدِيثٌ حَسَنٌ، رَوَاهُ الْبَيْهَقِيّ [في"السنن" 10/252]، وَغَيْرُهُ هَكَذَا، وَبَعْضُهُ فِي "الصَّحِيحَيْنِ".