If you meet the requirements below, you could potentially claim them as a dependent however since he has already claimed him on his taxes, you would have to prove to the IRS that he is your dependent. OR the child's father would have to file an amendment to remove his as a dependent.
The requirement to claim someone as a dependent (unless his mother release the right via IRS form), are listed in the below FAQ:
https://ttlc.intuit.com/replies/5187060