Can I create a Blockchain copy (up and running) in order to make my own bitcoins transfers without Fee? I need to make a lot of transfers per day (bitcoins), but the fee is higher than expected. I'm thinking in create a Blockchain copy running on our servers and make the transfers from my wallet and to my wallet by my own blockchain.

I'll charge my self a fee but small and fix.

That can be possible? or a missing something?

Thanks!
Anyone can create their own blockchain, but you will not be able to reconcile your chain with the bitcoin blockchain at a later date (even if you start your chain by forking off from a certain btc blockchain block height). 

I don't know what your use case is, but if you're not going to use an already existing blockchain, I would expect that creating a private database (SQL?) would be a better choice than trying to create a private blockchain. 

You could, for example, create a database that is designed to mimic the balances of bitcoin addresses you control. Users of your database could freely transfer these 'bitcoins' to eachother on your server, and then only when the user wants to move value to someone outside of your internal system, would you need to initiate an actual bitcoin network transaction. 

So the actual bitcoin you control would function as a 'reserve' that your database's value is backed by. This is basically how centralized exchange services work. The users of your system will need to trust you in using it.