The three kingdoms in China at the time of the attack by Genghis Khan were the Jin Dynasty, the Western Xia Dynasty, and the Southern Song Dynasty. These three kingdoms were significant political entities during the 13th century and played a crucial role in the Mongol conquest of China.

1. Jin Dynasty:
The Jin Dynasty was the ruling dynasty in northern China during the 12th and 13th centuries. It was established by the Jurchen people who overthrew the Liao Dynasty. The Jin Dynasty controlled a vast territory and had a strong military force. However, they faced constant threats from nomadic tribes in the north, including the Mongols led by Genghis Khan.

2. Western Xia Dynasty:
The Western Xia Dynasty, also known as the Tangut Empire, was situated in the northwest of China. It was founded by the Tangut ethnic group and existed from the 11th to the 13th century. The Western Xia Dynasty maintained a semi-nomadic lifestyle and had its own distinct culture and language. They often clashed with neighboring powers, including the Jin Dynasty.

3. Southern Song Dynasty:
The Southern Song Dynasty was the ruling dynasty in southern China from the late 12th century to the mid-13th century. It was established after the fall of the Northern Song Dynasty to the Jin Dynasty. The Southern Song Dynasty had its capital in Hangzhou and was known for its prosperous economy, sophisticated bureaucracy, and cultural achievements. However, they were constantly threatened by the Jin Dynasty in the north and faced internal conflicts.

Genghis Khan and the Mongol Empire:
Genghis Khan, the founder and leader of the Mongol Empire, launched a series of military campaigns in the early 13th century. His empire rapidly expanded, and he sought to conquer the Jin Dynasty, Western Xia Dynasty, and the Southern Song Dynasty. Genghis Khan's forces were highly skilled in warfare and utilized superior tactics, mobility, and horse archery.

The Mongols conquered the Western Xia Dynasty in 1227 and the Jin Dynasty in 1234. The fall of the Jin Dynasty enabled the Mongols to control northern China completely. However, the Southern Song Dynasty continued to resist Mongol invasions until its eventual downfall in 1279 under Kublai Khan, Genghis Khan's grandson. The Mongol conquest of China resulted in significant political and cultural changes, leading to the establishment of the Yuan Dynasty.

In conclusion, at the time of the attack by Genghis Khan, the three kingdoms in China were the Jin Dynasty, the Western Xia Dynasty, and the Southern Song Dynasty. Genghis Khan successfully conquered the Western Xia Dynasty and the Jin Dynasty, while the Southern Song Dynasty put up a prolonged resistance before succumbing to Mongol rule.