There are so many variables here that no one answer can be given. Every situation will be different. However, I would say (generally speaking) that there will be hardships. In light of this, let me make a few points.
First, even in families that have two committed parents there are struggles. So, if there is an unwed mother trying to raise her child on her own, the problems are compounded. If the mother is young and lacks maturity, there will be even greater difficulties. All of this might make these children feel insecure and perhaps even unloved at times. This can create various personality dysfunctions later in life.
Second, from a sociological point of view, the norm is still to have children in marriages. So, if a child is born out of wedlock (and there is no subsequent marriage), this might create a social stigma that might make the child feel different, unaccepted, and hence insecure. This can also have ramifications in the future.
Third, there will also be other factors, such as perhaps the lack of finances. As most people know that money is sometimes tight even when there are two working parents. This lack of finances might also lead to later issues.