In this context, "despite my best efforts" means that the father tried very hard to raise his son in a particular way, but the son turned out differently. The phrase suggests that the father may have had a specific vision or goal for his son's development, but the son's upbringing did not necessarily conform to that vision.
The phrase "best efforts" typically has a positive connotation, implying that the person has put in a lot of hard work and dedication towards a goal. However, in this particular case, the father is suggesting that his best efforts did not achieve the exact outcome he had hoped for, which may have led to some disappointment or frustration.
The father's following statement "credit to your mom" indicates that he recognizes and acknowledges the positive influence that the son's mother had on his upbringing, even if the father's own efforts did not lead to the exact outcome he desired.