Who are kaala-veditha? Is this is a class of humans or higher beings or is there a definite source for such information?
I am not sure if the term you have mentioned is Vedhita or Vidhata so hazarding an attempt to answer the question:
Kaal means time and Vidhata means organizer/arranger so basically the term refers to the gods of fate and there are two of those - Dhata & Vidhata.
Section LXVI of the Sambhava Parva of Mahabharat mentions their origin as follows:
And Brahman had two other sons, viz., Dhatri and Vidhatri who stayed with Manu. Their sister is the auspicious Lakshmi having her abode amid lotuses.
The Bhagvat Purana 1.4.1 also mentions the same:
Vashishth and his wife Arundhati begot seven Bramarishis like Chitraketu. Sage Atharva and his wife Chitti begot a son Taponishth. Great sage Bhrigu and his wife Khyati begot two sons- Dhata and Vidhata, and a daughter- Shri.
Therefore they are sons of Bhrigu and the grandsons of Brahma. The Mahabharat mentions them along with Varun as having attained salvation at the banks of Saraswati:
Again in the section where Jayadratha attempts to abduct Draupadi they are mentioned as divine beings at the level of Indra and Surya: