If I have 0.00603581 in my bitcoin wallet who much do I accually own ?
You own every bit of it. Assuming you have the private key for the wallet. As far as the blockchain network is concerned, anyone with the private key is the "owner" and will transfer those funds if the correct private key is provided in the transaction request.
As long as your private key remains private and you know what it is, you own it.
Now, to send that Bitcoin somewhere else, you'll have to pay a fee. That's why miners mine the blocks. So while you (assuming above conditions are satisfied) "own" every Satoshi inside that wallet, you'll need to pay to move it somewhere else.
Note: Nuances, subjective considerations and opinions have all been crushed for the sake of brevity.