For most of history, the successive dynasties which we retroactively call “China” never extended their official reach very far north. The histories of the various dynasties tell us that China always had northern neighbours who were often hostile: in the Han it was the Xiongnu, in the Song it was the Liao, Jurchens and later the Mongols, and in the Ming it was the Manchus (who eventually founded the Qing dynasty). These northern neighbours occupied the broad expanse of land which is Mongolia, northern China, and eastern Siberia today.

That being said, China's influence probably penetrated very far north. China traded extensively with its northern neighbours, exchanging technology, animals, and ideas. It's posited that the horse and the horse-drawn chariot was in fact an importation from northern tribes in a very early period. Similarly, a lot of Altaic (the language family many Siberian languages belong to) vocabulary and phonetics have made it into Chinese. China was undoubtedly the cultural centre of pre-modern East Asia, and any state or tribe worth its salt up north probably knew about China's existence and weight.

For a more specific and modern event regarding northern exploration, we can look to the early Qing dynasty.

In the second half of the seventeenth century, there was quite a lot of conflict between Chinese forces and Russian Cossacks in the Amur River region (just northeast of modern day Heilongjiang province; it is now under Russian jurisdiction). The Cossacks had, over the previous centuries, spread out from the West into much of Siberia. These warriors were now threatening the Chinese frontier. The Qing court sent at least two expeditionary forces up north (in 1654 and 1658) to combat the Cossacks, with the unlikely but pivotal help of trained musketeers from Korea. Eventually, the Russians were forced to concede the Amur region to China through the Treaty of Nerchinsk in 1689, which is why Qing dynasty maps show an entire chunk of Eastern Siberia as Chinese territory, including Vladvistock (https://i.pinimg.com/originals/8f/99/8f/8f998f755654e1842ed01d8b7306ae6b.jpg).

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General reading about China's interaction with the north:

Di Cosmo, Nicola. Ancient China and its Enemies: the Rise of Nomadic Power in East Asian History. Cambridge University Press, 2002.

Wang, Yuan-kang. "Explaining the Tribute System: Power, Confucianism, and War in Medieval East Asia." Journal of East Asian Studies 13.2 (2013): 207-232.

Su Bingqi and Yin Weizhang 苏秉琦、殷玮璋. “Guanyu Kaoguxue Wenhua de Quxi Leixing Wenti 关于考古学文化的区系类型问题." Wenwu 文物 5 (1981): 10-17. (If you can read Chinese)

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Reading about the Qing expeditions against the Cossacks:

Kang, Hyeok Hweon. "Big Heads and Buddhist Demons: The Korean Musketry Revolution and the Northern Expeditions of 1654 and 1658". Journal of Chinese Military History 2 (2013): 127–89