There are too many variables to give an answer to what adding a dependent to your tax return would do to your tax calculation.
For 2016, if you have not filed your return yet, complete your tax return without including your child. Note the refund or the balance due. Then go back to the Personal Info section and add your dependent. Compare the refund or balance due to what you had originally.
If you have already filed your 2016 tax return and for any prior year return that you have already filed, you can do a calculation for your own set of circumstances by going through the process of amending your tax return to include your dependent. The amended return will report the difference having a dependent in your tax return will make.
The proper way to handle this situation is for both you and the child's father to file amended tax returns for the years in question.
See the article below for instructions on how to amend a tax return.
https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed