I will answer as if you lived in Arizona, and as if you were either an adult or an emancipated minor (that is have moved out of your parent's homes and have been taking care of your own support needs.)

The child is the mother's unless and until the father gets some legal recognition as the father. This could be an order of paternity or a notarized document signed by both parties and his name placed on the birth certificate.

Without this, the father has no rights. With this the Court will presume that the child is in the custody of the Mother. The father may go to Court to ask for an appropriate order for Custody and Parenting Time.

In Arizona, and probably most other states, all Court orders relating to minor children must be "in the best interests of the minor child." The Court will assume that it is in the best interests of the child to have a close relationship with both parents. A willingness to share a child with the other parent is an indication that the parent who is willing will be better than a parent who makes threats to take the child away.

There are two kinds of custody: Legal and primary physical. Legal simply means that the person with legal custody makes decisions regarding education, religion and medical care. If there is joint legal custody, then the parties must consult together, and may have to agree. There is often a "tie breaker" in a joint custody order.

Primary physical custody deals with the household that the child spends most of its time in, where he or she keeps most of his or her stuff. Some parents will have a virtually equal custody arrangement. It depends upon the work and/or school schedules of the parties, or other obligations. It is best if parents can work out a shared parenting arrangement between themselves. The schedule that a Court may impose may not suit their individual lives as well as one that they can create.

In Arizona and in many other states there are classes that parents can take to show them what works and what doesn't work in shared parenting.

The bottom line is that your boyfriend cannot take your child away from you. The other side of the coin is that you cannot take the child away from him.