Laid down during the Carboniferous period, ~360 to ~300 million years ago.
Here "reptiles" is being used equivalently to "amniotes". The oldest fossil amniotes are of animals that were derived from amphibians, that is, non-reptile tetrapods.
The Carboniferous period is found in a later portion of the Paleozoic era, which in turn is found at the beginning of the Phanerozoic eon.
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