A 14-year-old lied to 21-year-old; had sex; got pregnant

Talk to an attorney. This is First Degree Statutory Rape, where the victim is 13, 14, 15 and the defendant is 6 or more years older than the victim, with a minimum of 144 months in prison (12 years) and a maximum of life (if the defendant has a very bad prior criminal record).

Your baby's father is clearly subject to prosecution for statutory rape.  Unfortunately, statutory rape is a "strict liability" crime.  That means that he can be convicted regardless of whether he actually knew that you were underage.  If he signs the birth certificate, his signature could be used as proof against him, and he could be charged.  I suggest that he consult with an attorney as soon as possible so that he can protect his rights as a parent while also protecting his rights from a criminal perspective.  Good luck.