I’d enroll him in the local subterranean elementary school, and teach him how to play Four-Square so he’d fit in with the other kids on the playground.
Backstory for the uninitiated:
Mike Mignola did a short two-pager about a very young Hellboy (who is, after all, the Apocalypse Beast, destined to lead the forces of Hell and the Outer Gods against Heaven, but was raised by humans and thus continually turns his back on his Infernal roots). It was a very cute story about how Hellboy was reluctant to try pancakes (“I HATE pamcakes!”) When he finally gave in and tried them, he, of course, loved them.
Cut to a scene in Hell, with the souls of the damned wailing even louder than usual. A Grand Duke of Hell (Haborym, IIRC) intones, “He has eaten the pancake. He is lost to us forever. Truly, this is our darkest hour.”
So you see, pancakes are the definitive cure for demonic chicanery and highjinks.
I would encourage his natural abilities, and steer him into a career in dentistry. He would worship me, though he probably has my destination wrong.
I’d totally wrap the thing in Kevlar and Goretex, put it on a leash and walk it around the neighborhood looking for fun with a “My kid will end humanity” bumper sticker on my ass.
I think that said baby and parents were dining (or terrorizing, I should say) at a restaurant where I had lunch the other day 
You KNOW your kid is a demon, when he priest at the Christening drops dead of a heart attack. Other bad signs: the child tries to kill you, and attarcts are large vicious dog. Being named “Damien” is laso bad.
Sorry,you HAVE to stab your baby through the heart with a silver dagger.
Hey, that was my plan!
What I always do is take the kid’s head and force it to rotate 360 degrees. If it can easily, then it’s a demon. So far I’ve been lucky in that I’ve had no demons. Unfortunately, no kid has yet to survive the test.
Admirably scientific. I wouldn’t worry too much about the shortcomings of the procedure. Every good method has its faults.
I’d teach him to be a ridiculously devout Christian, just for kicks, but make it obvious he’s still a demon. Mass confusion ensues, religious zealots get into redemption debates, the world implodes from the sheer wtfedness.
I’d take him to the mall, just like all of the other demon-baby owners.
Sorry, Dude, your beloved was a demon, not Satan. If he’s going to ever rule, it’s because he manages to oust the old guard.
Okay, I need a little more information before I can decide how I would raise the child.
So, that means I’m single, right? Was the mother hot? Can I call all her demon girlfriends and talk about what a rotten mommy she was and get them to sleep with me out of sympathy?
Does the demon-child have any obvious defects or talents that would impress mortal women or gain sympathy? Is there any way to convince them that if I can do this good a job with an actual demon I’d be an exceptionally good father to a homo sapien* child?
Obviously, my first concern is the emotional and spiritual well being of the child, homo sapien or not. I’m just trying to figure out the parameters of the rest of my life.
- since we are talking about both my child and my now-ex-wife, I think we should be less cavalier about throwing around the phrase “human” in quite such a judgemental way. I may have banged a creature from the infernal regions, but that doesn’t mean I don’t have a sensitive side.
I’d learn whatever magic, alchemic, or spiritual enchantments were needed to keep him from pulling my heart out of my chest and eating it still beating.
Then once I had reasonable control I’d raise him like any other kid. While reflecting how much better his mom still was then my recent ex.