Unfortunately this is a period of Chinese history which is left understudied in many areas. It is also extremely chaotic, but has been pieced together throughout time. Some good books to start off of with:

Warlord Politics, Lucian Pye (good overview)

The Military-Gentry Coalition, Jerome Chen

Warlord Politics in China, 1916-1928, Hsi-Sheng Ch'i

Warlord Soldiers, Diana Lary

Chang Tso-Lin in Northeast China, Gavan McCormick (Japanese influence in NE China)

Warlords and Muslims in Chinese Central Asia, Andrew Forbes (Ma Clique)

Yuan Shikai: A Reappraisal, Patrick Shan

The Power of the Gun, Edward McCord

Maybe a little China: How the Empire Fell, by Esherick to get some background on the events leading up to the Warlord period.

Of course, the "Warlord period" is a pretty broad area of study. Much research involving this period is far more focused on the events that shape modern China, such as the May Fourth Movement. As a result, some of the works (like Pye & Chen) specifically targeting the warlords are very dated and perhaps esoteric. I tried adding in some newer sources in there like Shan's work on Yuan Shikai (a precursor to the Warlord period, technically, but still a very important figure for it).

There are also a lot of works dealing primarily with the Republican period that touch on the warlord period, but don't do it as much justice. You can also try scanning JSTOR there are probably some decent articles on there.

Feel free to ask any questions.

Firstly, some foundational texts on Warlord China:

Lary, Diana. "Warlord studies." Modern China 6, no. 4 (1980): 439-470.

Chi, Hsi-Sheng. Warlord politics in China, 1916-1928. Stanford: Stanford University Press, 1976.

McCord, Edward. The power of the gun: The emergence of modern Chinese Warlordism. Berkeley: University of California Press, 1993.

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On warlord governance:

Alfred H. Y. Lin, ‘Building and Funding a Warlord Regime: The Experience of Chen Jitang in Guangdong, 1929-1936’, Modern China 28:2 (2002).

Suleski, Ronald Stanley. Civil government in warlord China: tradition, modernization and Manchuria. New York: Peter Lang Publishing, 2002.

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I’m most familiar with USSR involvement in Republican Xinjiang:

Forbes, Andrew D.W. Warlords and Muslims in Chinese Central Asia: A Political History of Republican Sinkiang 1911-1949. Cambridge: Cambridge University Press, 1986.

Jacobs, Justin M. Xinjiang and the Modern Chinese State. Washington, D.C.: University of Washington Press, 2016.

Kinzley, Judd C. Natural resources and the new frontier: constructing modern China's borderlands. Chicago: University of Chicago Press, 2018.

Whiting, Allen S. and Sheng, Shi-cai. Sinkiang: Pawn or Pivot? East Lansing, Michigan: Michigan State University Press, 1958. [note that this is a primary source - Sheng Shi-cai was the leading warlord in Xinjiang during 1933-1944, and his take on events SHOULD NOT be taken as fact]

If you're interested in the primary sources themselves, the Wilson Center has translated documents on Soviet involvement in Xinjiang accessible for free without registration here. There's some material on Ma Zhong-ying's (member of the Ma Clique) actions in Xinjiang in the collection as well.

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Unfortunately, I don’t think anyone’s done a study of the Ma Clique in English.