The Maturidi Madhhab developed further over the 200 years following the death of Abu Mansur al-Maturidi, mainly through teaching as opposed to writing and authoring.
The students of al-Maturidi became a kalaamist faction that arose first in Samarqand, and they were Hanafi in their fiqh (jurisprudence). Its adherents strove to spread the ideas of al-Maturidi, who was their Imaam, and it remained prominent in those lands, and, in later centuries, in the lands of Afghanistan and the Indian sub-continent. The most prominent figures in this period were Abu al-Qasim Ishaaq bin Muhammad bin Ismaa'eel al-Hakeem as-Samarqandee (d. 342H) and Abu Muhammad Abdul-Kareem bin Eesaa al-Bazduwi (d. 390H).
The fifth century after hijrah, 400H onwards, was still the formative period, and prominent figures in this century were Abu al-Yusr Muhammad bin al-Husain ibn Abdul-Kareem al-Bazduwi (d. 493H), and he was a Shaykh of the Hanafis in his time. His grandfather was Abdul-Kareem al-Bazduwi (d. 390H) mentioned above. He read the books of the Philosophers like al-Kindi and the books of the Mu'tazilah such as those of al-Ka'bee, al-Jubaa'ee and an-Nadhaam and prohibited from looking into them due to what they may cause of doubts. He also studied the works of al-Maturidi and rewrote them with better order and organization.
A large number of students took from Abu al-Yusr, and from them his son, al-Qaadee Abu al-Ma'aanee Ahmad, and Najm ud-Deen Umar bin Muhammad an-Nasafee, the author of "al-Aqaa'id an-Nasafiyyah" and others.
In this early period there was not much in the way of codification and formalization through written works. That took place over the next two centuries, from 500H onwards.