You didn't say whether your father files a tax return. Even though he doesn't work, he might have income. If he does file a tax return, he might be able to claim you as a dependent if you did not provide more than half of your own support for the year. If your father can claim you as a dependent, you cannot claim any dependents on your tax return.

If your father cannot claim you as a dependent, you can claim your son as a dependent on your tax return. When you enter the information about your son in TurboTax, read all of the questions carefully. One question will ask how many months your son lived with you in 2018. If he was born in 2018, select "The whole year." The next question will ask whether your son provided more than half of his own support. It's not asking you whether you supported him. That doesn't matter. It's asking whether he provided his own support. I assume he didn't, so you would answer No.