I have committed Zina with an American girl and now she is pregnant and she wants to have an abortion. I don't know what to do. Should I let her have the abortion or should I have the baby of Zina? She doesn't want to marry me! Please tell me what to do, because the baby is (Ibn Zina) and I don't want to have Ibn Zina!

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

You should make sincere repentance to Allah, ask His forgiveness as much as possible, and continue doing good deeds and supererogatory acts of worship. Moreover, avoid being with bad friends; rather, befriend pious and righteous persons. You should completely avoid this woman who combines between two repulsive characteristics: Kufr (disbelief) and prostitution. Allah Says (what means): {And when you see those who engage in [offensive] discourse concerning Our verses, then turn away from them until they enter into another conversation. And if Satan should cause you to forget, then do not remain after the reminder with the wrongdoing people.} [Quran 6:68]

Marrying her is not permissible as Allah Says (what means): {The fornicator does not marry except a [female] fornicator or polytheist, and none marries her except a fornicator or a polytheist, and that has been made unlawful to the believers.} [Quran 24:3]

Know also that demanding her to abort her fetus is also not permissible if the pregnancy has passed forty days.
However, if you can stop her from aborting her fetus you are obliged to do it. Occurrence of the pregnancy from Zina is not a valid excuse to abort it but any co-operation for doing so is not permissible regardless of how serious its results are. What is the crime of the fetus hence to abort it? No doubt, aborting a fetus is an aggression against a soul, which is already created by Allah. This practice never erases the sin of Zina, but rather adds to it another crime; i.e. abortion.

Allah does not like mischief in His earth. Furthermore, keep in mind that you do not have any relation to that child of Zina, so he/she should not be traced back to you for lineage or inheritance. Whenever you see him/her you should repeat your repentance to Allah and increase asking Allah's forgiveness.

Allah knows best.