9 events the sources record for this year, grouped by region.
What happened
China (2)
Mongol troops enter Taeju, kill the magistrate Choe Je, and take his wife and children captive; many residents suffer. (Goryeosa (History of Goryeo) 世家 卷24 高宗 四十四年)
In the first month the Mongol Dong Wenwei built walls at Guanghua and Zaoyang, stored supplies, and attacked Xiangyang and Fancheng together; to the south they relied on the Han River, to the north they were blocked by the lake, and in the end they could not cross. (Xu Zizhi Tongjian (Continuation of the Comprehensive Mirror) 권175 正月 단락175.7.0)
Korean Peninsula (2)
Wonju bandits An Yeol and others take Gosong and rebel; the general Yun Gun-jeong and the nangjang Gwon Chan lead troops to suppress them. (Goryeosa (History of Goryeo) 世家 卷24 高宗 四十四年)
Six Mongol ships raid Changnin Island, and Yi Su-song, magistrate of Ongjin, drives them off with the Byeolcho. (Goryeosa (History of Goryeo) 世家 卷24 高宗 四十四年)
Southeast Asia (3)
The Yuan general Uliangkatai invaded Pingliyuan, and the emperor personally oversaw the fighting. (Đại Việt sử ký toàn thư 本紀卷之五 「丁巳七年春二月，黄炳挈家詣闕，進」)
The emperor and the crown prince met them at Đông Bộ Đầu with galley ships and inflicted a great defeat. (Đại Việt sử ký toàn thư 本紀卷之五 「丁巳七年春二月，黄炳挈家詣闕，進」)
Uriyangqadai attacked Jiaozhi and entered that country; the ruler of Annam, Tran Nhat Canh (陳日煚), fled to an island at sea. (History of Yuan (Yuanshi), Annals 元史 卷3 憲宗 1257年 11月)