The following is written with some sarcasm....
As far as you not signing anything....good luck with that. You don't have to sign anything to be on the birth certificate. The mother of the child can put you on there....its your responsibility to prove that you are not the child's natural father. That may mean going to court and getting a court ordered paternity test, which could take months, while your child support starts at birth.
Also, even if you are a student and not working, many times you will be responsible for paying a percentage (usually anywhere from 20-35 percent, depending if the child has special needs) of what a normal person would working forty hours a week. Also, if your baby's momma is working, you could be responsible for half of the daycare expense for the hours that she works or in school, on top of regular child support. You also could be responsible for providing medical and dental insurance for the child.
If you should happen to fall behind in child support, as stated above, you will go into arrears and possibly to jail if you fall behind enough. If you are behind in your child support you might be able to take the bar exam, but you will NOT be able to enter the military.
Once you are in the military, thats where the fun begins. You will be an O2 (LT) for about six months. The current O2 base pay is 2844 a month. BAS is 192 a month. Now your BAH (housing allowance) will depend on where you live. Lets say it will be about 1500 a month, which is average. Thats 4536 a month. Your child support will fall anywhere from about 1000-1600 a month. Dont worry about paying it, it will automatically be deducted from your check every month, you wont even have to see it! Your child will have free medical coverage, and dental is only like 25 bucks a month.
The best part of all this is that you have NO say in where the child support money goes. Anything that you give directly to the child is not counted in child support. The best thing to do, if you are the dad, is to go to court for child support right away, or have the local child support office figure it out for you, and they can have a judge sign it. Then, make arrangements to PAY THE STATE DIRECTLY. People do this (myself included) because the mother can be dishonest and say "I never got the money" and you find yourself in arrears.
Seriously though, be a man and step up and face your responsiblity, both financially and morally. You should to be in the child's life and be a good dad. You may have to put law school off for a bit or go part time. Your law career might work out and it might not...but your child will always be there.