I need study to implement a public-private DLT system more like hyperledger but without the elevated cost of implementation - transaction, because is a study project
You can take a look at this first https://chrysalis.docs.iota.org/introduction/what_is_chrysalis.html
Recently IOTA has released their specification. This would be the best reading material but it is not necessarily easy.
But you can probably just use the public ledger or the dev net depending on your needs. The only real reason I can think of implementing your own private IOTA ledger is if you wanted to store all the data and you did not want any other people's data being stored. Currently on the IOTA ledger the data is not guaranteed persistent forever, as there is pruning.
To implement your own private tangle you will want to activate the coordinator plugin in the hornet node:
It does not seem as well documented as it used to be.
You can also check out the many blog posts to get a high-level understanding and liks to details: https://blog.iota.org/tag/chrysalis/