What if the bio-father doesn't have capability to support financially the child?

What if? Child support is determined according to a formula that includes his income.

If the father can't help support the child, then you have to rely on other sources, Family, social services, etc.

It is not abandonment, the father is only required to do what the law requires. If he has no job, then there may be no support ordered by the court, or it will only be a very small amount owed each month.

It does not take away the fathers rights or stop his rights for visitation.