As Coolcryptovator said, the OP is completely unclear and it would be difficult for us to give a solution for your question.

Let me try to help you as far as I have understood the question  

Download the latest version of bitcoin core from https://bitcoin.org/en/download Once you have done so, run the client and the whole blockchain will be downloaded. The first block to be downloaded is the genesis block.

etter to follow the topic and build an older version of core.

This is false. Private keys are not related to generating a new block. Private keys are used to spend the coins and they won't be exposed when a miner mines a block or when a programmer generates a new genesis block.