Certainly. While I'm not familiar with the book written by P.M. Barford, there has been a range of works on the early Turkic people in both English and other languages.

The most important one, I find is a Russian work:

• Gok-Turk by L. N. Gumilev

Written during the Soviet period it is a product of Marxist thought but it is vital in understanding the early Turkic people.

A standard product in all Central Asian libraries should be:

• The Empire of the Steppes: A History of Central Asia written by Rene Grousset

It has been translated into English. While much of the scholarship is out of date, it is still valuable in building the foundation of knowledge necessary to read about this era.

Another standard foundational work would be the six volume

• *History of Civilizations of Central Asia

Though you may need only one or two volumes of this set

For those Turkic groups who remained East and had more interactions with China, I would suggest:

• The Perilous Frontier: Nomadic Empires and China, 221 BC to AD 1757 by Thomas J. Barfield
• Peace, War, and Trade Along the Great Wall: Nomadic-Chinese Interaction through Two Millennia by Thomas J. Barfield
• Eurasian Crossroads: A History of Xinjiang by James A. Millward
• The Cambridge History of China Volume III Part I and Volume VI
• Ancient China and its Enemies: The Rise of Nomadic Power in East Asian History by Nicola Di Cosmo

For stuff written in Uyghur about the Turkic world I suggest:

• Chagatai Uyghur Tili Haqqida by Musasal Bayan

For Turkic groups who when to the Middle East prior to the Seljuks I would suggest:

• The Breaking of a Thousand Swords: A History of the Turkish Military of Samarra (A.h. 200-275/815-889 CE) by Matthew S. Gordon

To examine the Turkic groups who migrated west, I would suggest:

• The World of the Huns: Studies in Their History and Culture by Otto J. Maenchen-Helfen
• The Bulgars and the Steppe Empire in the Early Middle Ages: The Problem of Others by Tsvetelin Stepsou
• Pechenegs, Cumans, Iasians: Steppe peoples in Medieval Hungary by Andras Paloczi Horvath
• Treasure of the Land of Darkness: The Fur Trade and its Significance for Medieval Russia by Janet Martin

I Would also suggest these works:

• A History of Russia, Central Asia, and Mongolia: Volume I Inner Eurasia from Prehistory to the Mongol Empire by David Christian
• • The Cambridge History of Early Inner Asia* edited by Denis Sinor
• The Heritage of Central Asia: From Antiquity to the Turkish Expansion by Richard N. Frye
• Imperial Nomads: A History of Central Asia 500-1500 by Luc Kwanten