Question
Did our scriptures mention any avatar that Parabrahma has taken?
Answer
Yes, certainly. But NOT in the same sense as of those of say, Lord Vishnu or Lord Shiva. The reason for this is that the nature of the Parambramhm (Parbramha) is fundamentally different from that of both - ordinary souls like us, who are linked to casual ( and ultimately to gross ) bodies, as well as the divine souls residing in the higher realms.
In particular,
The gross forms which we refer to as incarnations, exist as material personifications of the divine beings ( read Gods ), who in spite of there divinity, are incomplete aspects of the Supreme Brahma, just like us ( except when they are in yoga with the Consciousness , of course ) .
There incarnations are therefore aspects of and by extension casual incarnations of Parbramha.
Being the 'casual actor' responsible for the the apparent existence of the worlds and beings, it is clearly absurd to speak of there being a personification of the Brahma in one gross body more than in any other, with the possible exception of the divine beings and their incarnations.
All the above points have been sufficiently reconfirmed by both sages and scriptures, for there to be any need for a citation.
TL;DR
Clearly, it is impossible to find a scriptural reference to an avatar of the kind you enquired about ( not TOO sure about this ) . However, it is true that these exist and that we are among them.
Note: “The question: Did our scriptures mention any avatar that Parabrahma has taken?” is licensed by Stack Exchange Inc (https://hinduism.stackexchange.com/); user contributions licensed under CC BY-SA.