Jin China covered the northern half of China, as opposed to southern Song China.
Its history started to diverge from OTL in 1211 / 2908, Yin Metal Sheep (Chinese Calendar) when the Khitan chief Yelü Liuge didn't revolt in Liaodong, and the general (and IOTL later warlord) Puxian Wannu didn't have to fight him.
1213 (2910, Yin Water Chicken), Jin emperor Wányán Yongjì wasn't killed, continued to reign twenty more years instead.
In 1214/15 (2911, Yang Wood Dog / 2912, Yin Wood Pig), the Jin didn't move their capital to Kaifeng, as they did IOTL due to the Mongol threat. and of course, in 1234 (2931, Yang Wood Horse) the Jurchen / Jin Empire didn't fall.
1235 (2932, Yin Wood Sheep), Wányán Yongjì died and was replaced by Wányán Shouxù.
In 1244 (2941, Yang Wood Dragon), the Jin empire demanded from the Hsi-Hsia to pay them tribute. When the Tangutes (who had suffered under Ogadai Khan's attacks only a few years ago) declined, the Jin decided to make war, which began 1247 (2944, Yin Fire Sheep). 1256 (2953, Yang Fire Dragon), the Hsi-Hsia were incorporated into Jin China again.
On September 27th 1290, (2987, Yang Metal Tiger), the Earthquake in Chihli (Province Hopeh) happened, 150,000 people were killed. (Even more than IOTL, since the Mongols didn't kill half of North China's population.)
During 1353-59 (3050, Yin Water Snake / 3056, Yin Earth Pig), the Black Death swept through North China.
Meanwhile, in the south the kingdom of Hong had replaced the Song. In 1358 (3055, Yang Earth Dog), the Jin empire demandes from the Hong emperor to pay tribute. He gave in, for the moment. But in 1381 (3078, Yin Metal Chicken), Hong China stopped paying tribute to the Jin. A new war started. It proved now, however, that Jin China, although it seemed to be strong on the outside, depended too much on mercenaries.
1384 (3081, Yang Wood Rat), the Hong emperor made peace because of unrest in Szechuan and the southern provinces demanded his undivided attention. Jin China just ceded Kaifeng and Luoyang. But in 1387 (3084, Yin Fire Rabbit), the War between Hong and Jin started again. In addition, 1390 Goryeo entered the war on Hong China's side against Jin.
1392 (3089, Yang Water Monkey), the Hong conquered Beijing, the Jin empire was destroyed. The surviving Jin leaders were decapitated.